Chess and Individual Differences 110847604X, 9781108476041

Table of contents :
Cover
Half-title page
Title page
Copyright page
Contents
List of
Figures
List of
Tables
Preface
Acknowledgements
1 Introduction
1.1 A Very Brief Opening to the Game of Chess
1.2 Overview of This Book
2 Quantifying Chess Skill
2.1 Elo Rating Lists
2.2 Updating Mechanism and Basic Statistics of the Elo Rating
2.3 Alternatives to the Elo Rating of Chess Players
2.4 Overview of Studies Using the Elo Rating
3 Cognition
3.1 Perception
3.2 Memory
3.3 Thinking
4 Individual Differences
4.1 Characterization and Appraisal of Individual Differences
4.2 Individual Differences in Chess
4.3 Heredity versus Environment
5 Psychophysiology and Brain Functioning
5.1 Psychophysiology and Chess
5.2 Brain Basics
5.3 Electroencephalography (EEG)
5.4 Overview of Brain-Imaging Studies
5.5 Cerebral Cortex Areas
5.6 Hemispheric Specialization
5.7 Other Brain Areas and Anatomical Changes
5.8 Summarizing Findings about Brain Functioning and Chess
6 Intelligence
6.1 Approaches to the Study of Intelligence
6.2 Individual Differences in Intelligence and Chess
6.3 Intelligence and Chess in Children
6.4 Intelligence and Chess in Adults
6.5 Summarizing Findings about Intelligence in Chess
6.6 Chess Skill versus Chess Motivation in Predicting Chess Performance
7 Personality
7.1 Approaches to the Study of Personality
7.2 Personality and Chess-Playing Style
7.3 Personality Factors Studied with Chess Players
7.4 Personality, Motivation, Emotional Regulation, and Chess Knowledge
8 Expertise
8.1 The Role of Practice
8.2 Talent versus Practice
8.3 Cognitive Decline in Chess
9 Sex Differences
9.1 Sex Differences in Intelligence and Personality
9.2 Sex Differences in Science, Technology, Engineering, and Mathematics (STEM)
9.3 Sex Differences in Participation Rates in Chess
9.4 Sex Differences in Chess Playing
9.5 Sex Differences in Chess Performance at Different Levels of Practice
10 Applications
10.1 Business
10.2 Health
10.3 Education and School
10.4 Transfer
10.5 Statistical Power
11 Concluding Remarks
Appendix 1
Appendix 2
Appendix 3
Appendix 4
Glossary
References
Index

Citation preview

CHESS AND INDIVIDUAL DIFFERENCES

Research from the neurosciences and behavioural sciences highlights the importance of individual differences in explaining human behaviour. Individual differences in core psychological constructs, such as intelligence or personality, account for meaningful variations in a vast range of responses and behaviours. Aspects of chess have been increasingly used in the past to evaluate a myriad of psychological theories, and several of these studies consider individual differences to be key constructs in their respective fields. This book summarizes the research surrounding the psychology of chess from an individual- differences perspective. The findings accumulated from nearly forty years’ worth of research about chess and individual differences are brought together to show what is known – and still unknown – about the psychology of chess, with an emphasis on how people differ from one another. Angel Blanch works in the Department of Psychology at the University of Lleida, Catalonia, Spain. His research focuses on individual differences, intellectual performance and data analyses in behavioural science. Angel also serves as an associate editor at Personality and Individual Differences, as well as advising on the editorial board for Psychological Assessment and Stress and Health.

CHESS AND INDIVIDUAL DIFFERENCES ANGEL BLANCH Universitat de Lleida

University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781108476041 DOI: 10.1017/9781108567732 © Angel Blanch 2021 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2021 A catalogue record for this publication is available from the British Library. Library of Congress Cataloging-in-Publication Data Names: Blanch, Angel, 1967– author. Title: Chess and individual differences / Angel Blanch, Universitat de Lleida. Description: New York, NY : Cambridge University Press, 2021. | Includes bibliographical references and index. Identifiers: LCCN 2020031750 | ISBN 9781108476041 (hardback) | ISBN 9781108567732 (ebook) Subjects: LCSH: Chess – Psychological aspects. | Chess – Social aspects. | Pattern perception. | Individual differences. Classification: LCC GV1448 .B53 2021 | DDC 794.1–dc23 LC record available at https://lccn.loc.gov/2020031750 ISBN 978-1-108-47604-1 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

CONTENTS

List of Figures List of Tables Preface Acknowledgements 1

2

Introduction

1

1.1 A Very Brief Opening to the Game of Chess 1.2 Overview of This Book

1 4

4

5

9

Quantifying Chess Skill 2.1 2.2 2.3 2.4

3

page vii x xii xiii

Elo Rating Lists Updating Mechanism and Basic Statistics of the Elo Rating Alternatives to the Elo Rating of Chess Players Overview of Studies Using the Elo Rating

10 11 15 17

Cognition

19

3.1 Perception 3.2 Memory 3.3 Thinking

20 25 30

Individual Differences

38

4.1 Characterization and Appraisal of Individual Differences 4.2 Individual Differences in Chess 4.3 Heredity versus Environment

39 45 51

Psychophysiology and Brain Functioning

57

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

58 60 62 65 81 83 85 87

Psychophysiology and Chess Brain Basics Electroencephalography (EEG) Overview of Brain-Imaging Studies Cerebral Cortex Areas Hemispheric Specialization Other Brain Areas and Anatomical Changes Summarizing Findings about Brain Functioning and Chess

v

vi

contents 6

Intelligence 6.1 6.2 6.3 6.4 6.5 6.6

7

8

9

10

11

Approaches to the Study of Intelligence Individual Differences in Intelligence and Chess Intelligence and Chess in Children Intelligence and Chess in Adults Summarizing Findings about Intelligence in Chess Chess Skill versus Chess Motivation in Predicting Chess Performance

89 93 97 102 107 110 112

Personality

118

7.1 7.2 7.3 7.4

120 124 126

Approaches to the Study of Personality Personality and Chess-Playing Style Personality Factors Studied with Chess Players Personality, Motivation, Emotional Regulation, and Chess Knowledge

130

Expertise

135

8.1 The Role of Practice 8.2 Talent versus Practice 8.3 Cognitive Decline in Chess

138 146 151

Sex Differences

157

9.1 Sex Differences in Intelligence and Personality 9.2 Sex Differences in Science, Technology, Engineering, and Mathematics (STEM) 9.3 Sex Differences in Participation Rates in Chess 9.4 Sex Differences in Chess Playing 9.5 Sex Differences in Chess Performance at Different Levels of Practice

159

Applications

181

10.1 10.2 10.3 10.4 10.5

181 184 187 194 196

Business Health Education and School Transfer Statistical Power

162 164 169 171

Concluding Remarks

201

Appendices Glossary References Index

207 249 254 291

FIGURES

1.1 A chess game with all intervening pieces in action (left diagram); a chess problem with white to play and win (right diagram; taken from a game between Velmirovic and Csom in Amsterdam, 1974) 2.1 Elo rating lists of the World (a), Spanish (b), and Catalan Chess Federations (c), and Elo rating list of top twenty-eight computer chess engines out of a list of 353 engines (d) 2.2 Density plot of the Elo rating with normal (continuous line) and logistic (dotted line) distributions 2.3 Density plots for the distribution of the Elo ratings in the age of participants (a), number of games (b), tournament outcome (c), and Elo rating (d) of four chess tournaments 3.1 The representation of a chess tree with 86 nodes begins in the black central node, which splits into three main variants (dotted lines); each successive node splits into three lower-level nodes, representing the alternative choices arising at each main variant 4.1 A structure of personality impressions from a multidimensional scaling approach (Rosenberg, Nelson, & Vivekananthan, 1968) 4.2 A simple classification of psychological traits into two broad dimensions: intelligence and personality 4.3 There are different levels of analysis and measurement in differential psychology; the levels of analyses (traits, processes, and biological) can be combined to analyse the variability in a given target behaviour 4.4 Cross-sectional, longitudinal, and sequential research designs to evaluate inter-individual variability 4.5 The PPIK theory applied to the chess domain (intelligence as process, personality, interests, intelligence as knowledge: Ackerman, 1996); Gf = fluid intelligence; Gc = crystallized intelligence; TIE = typical intellectual engagement

vii

page 2

11 14

15

20 42 42

43 44

47

viii

list of figures

4.6 Sample items from the Amsterdam Chess Test in the choose-a-move, predict-a-move, and recall subtasks (van der Maas & Wagenmakers, 2005) 49 5.1 Diagram (a): the four main lobes of the human cerebral cortex: frontal, parietal, temporal, and occipital. The main functions of the cerebral cortex are (frontal lobes): motor skills, voluntary movement, speech, problem solving and judgement; (parietal lobes): sensory awareness, symbolic communication, and abstract reasoning; (occipital lobes): visual processing; (temporal lobes): visual memory, recognition of objects and faces, and verbal memory for the use of language (reproduced with permission from the American Psychological Association). Diagram (b): the 10–20 system for the recording of electroencephalograms (EEGs) in humans, showing the reference electrodes nasion (NZ) and inion (IZ), and electrodes corresponding to the cerebral cortex lobes, frontal (F), temporal (T), parietal (P), and occipital (O); the amount of electrodes can vary depending on the research aims and kind of equipment 61 6.1 The normal distribution with IQ scores compared with the approximate percentage of cases under the curve, and other scoring systems 93 6.2 Hierarchical (Carroll’s model) and non-hierarchical (Thurstone’s model) psychometric models of human intelligence; the squares in both models represent the specific tests used to measure each broad factor 96 6.3 Structural equation model evaluating the impact of chess skill (Elo rating) and motivation, on tactical (T), positional (P), and endgame (E) chess performance; observed variables are represented with squares, latent (unobserved) variables are represented with ellipses; one-headed arrows represent causal links, the two-headed arrow a correlation; there were twelve degrees of freedom for Model 1, and fifteen degrees of freedom for Models 2 and 3 (CFI = comparative fit index; TLI = Tucker–Lewis index; RMSEA = root mean squared error of approximation; AIC = Akaike information criterion) 115 7.1 Eysenck’s PEN (psychoticism–extraversion–neuroticism) and Gray’s RST (reinforcement sensitivity theory of personality) models of personality 122 7.2 Structural equation model with observed variables to predict the Elo rating, from age, verbal chess knowledge (openings, positional, endgame, visualization), personality factors (extraversion, neuroticism, psychoticism), chess motivation, and emotional regulation (cognitive reappraisal, expressive suppression); all correlation coefficients (double-headed arrows) were significant at the p < 0.05 level. The exogenous variable e1 represents an error term 133 8.1 The power law in action in six information-processing tasks: mirror tracing, reading inverted text, scanning visual targets, sentence recognition, an online editing routine, and geometry proof justification. The Y axis shows the time (seconds) invested in completing the task, the X axis

list of figures

8.2

9.1

9.2

9.3

represent 100 trials in each task. The empirical parameters (a and b) are those as suggested in the study by Newell and Rosenbloom (1981) Association of age with the predicted Elo rating at three levels of expertise: FIDE masters (white colouring), international masters (grey), and grandmasters (black). Triangles represent men, and circles represent women (data: FIDE list, March 2014) Female observed ranks (black dots) compared with the expected rank (straight line), discontinuous lines representing the 0.05 and 99.95 quantiles; male to female ratios (M:F) are shown next to each country name Discrepancy in actual and estimated sex differences in Elo rating points for twenty-four Eurasian countries: Azerbaijan, Belarus, Bulgaria, Croatia, the Czech Republic, England, France, Georgia, Germany, Greece, Hungary, Italy, Lithuania, the Netherlands, Poland, Portugal, Romania, Russia, Serbia, Slovakia, Slovenia, Spain, Turkey, Ukraine Elo ratings for men (black triangles) and women (white circles) at twelve, six, three, and two levels of practice; the horizontal dotted line represents 2000 Elo points

ix 140

155

167

168

178

TABLES

1.1 Overview of the two main approaches to psychological research page 2 2.1 Example of the Elo rating updating in one chess game between players KS versus AB, and JP versus LQ 13 2.2 Descriptive statistics of the Elo ratings in four chess tournaments 16 3.1 Information-processing models to explain perceptual processes in chess (EPAM = elementary perceiver and memorizer; MAPP = memory-aided pattern perceiver) 22 3.2 Overview of theories addressing the role of expert memory in chess (LTM = long-term memory; SEEK = search, evaluation, knowledge) with the degree of supportive and unsupportive evidence (Gobet, 1998) 26 5.1 Studies in brain functioning in chess players (EEG = electroencephalography; MEG = magnetoencephalography; fMRI = functional magnetic resonance imaging; PET = positron emission tomography; SPECT = single-photon emission computerized tomography). In the N column, ‘M’ denotes that all participants were males, and ‘F’ denotes the number of females 66 6.1 Overview of some tests to evaluate cognitive abilities 91 6.2 Theories and approaches to the study of human intelligence 94 6.3 Unofficial and official world chess champions and additional intellectual activities 99 7.1 Factors (in boldface) and facets of the five-factor model (FFM) measured with the NEO-PI-R instrument 121 7.2 Comparison of verbal chess knowledge, chess motivation, personality factors, emotional regulation, and the Elo rating in chess players and in the general population (normative data for extraversion, neuroticism, and psychoticism: n = 527; normative data for verbal chess knowledge, chess motivation and Elo rating: n = 259; normative data for cognitive reappraisal and expressive suppression n = 1,483; chess players: n = 100) 132 8.1 Achievements and shortcomings of experts (Chi, 2006a), and good performance and poor performance of experts in accordance with task characteristics (Shanteau, 1992, 2015) 136

x

list of tables 8.2 Practice impact and determinants of individual differences in expert performance in accordance with the type of task (Ackerman, 2007). Differential effective strategies refer to tasks that can be completed successfully with different strategies. Inconsistent information processing refers to acquiring different skills to complete the same task. Closed tasks are bounded by a finite domain of knowledge, whereas open tasks are unbounded and cumulative 9.1 Cognitive tasks and tests showing sex differences (adapted from Halpern, 1997) 9.2 Means, standard deviations (Sd) and t-tests in number of games, and Elo ratings for 600 men and women chess players. Layer 1 has twelve levels with fifty men and fifty women; layer 2 has six levels with 100 men and 100 women; layer 3 has three levels of 200 men and 200 women; layer 4 has two levels of 300 men and 300 women 10.1 Overview of studies describing a chess instructional intervention for schoolchildren (M:F = male to female ratio) 10.2 Post-hoc analyses of statistical power (1 – β) of studies describing a chess instructional intervention for schoolchildren (d = 0.5 and 0.8, α = 0.05). The studies with only one sample size conducted comparisons of experimental and control groups of equal sample sizes

xi

138 160

175 190

198

PREFACE

A considerable body of research within several fields of neurosciences and behavioural sciences has highlighted the crucial importance of individual differences in explaining human behaviour. Individual differences in core psychological constructs such as intelligence or personality account for meaningful variations in a vast diversity of responses and behaviours. Some aspects of the game of chess have been used in the past to evaluate a myriad of psychological theories. Several of these studies consider individual differences as key constructs in their respective fields of research. This book summarizes the latest research about the psychology of chess from an individual differences approach. The volume provides a comprehensive overview of the findings accumulated through nearly forty years of research into chess and individual differences. This volume, Chess and Individual Differences, organizes a complete perspective in terms of what is already known and what remains unknown about the psychology of chess, with an emphasis on individual differences.

xiii

ACKNOWLEDGEMENTS

Writing this book would have been impossible without the help of the Cambridge staff. In particular, I am gratefully indebted to Janka Romero, Emily Watton, and Jessica Norman for providing assistance throughout the process. Special thanks go to Guillermo Campitelli, who elaborated extensive and priceless feedback on an earlier draft of the manuscript. My greatest debt, however, is to my wife, Loles, and to my two-year-old daughter, Petra, who stoically withstood the time and effort spent on the book and gave me comfort in the meanwhile.

xiv

1 Introduction

Several facets of the game of chess have been used in the past to model and evaluate a myriad of psychological theories in a variety of empirical studies. Most of these studies have taken either an experimental or a correlational approach (Table 1.1). Over half a century ago Lee Cronbach examined in detail the evolution of empirical psychology stemming from these two lines of work (Cronbach, 1957). Cronbach contended that a combination of the experimental and correlational approaches would be the most rewarding for advancing psychology, in both basic and applied research. Analogous arguments have repeatedly been brought up, while advocating for a greater degree of cooperation between cognitive scientists and differential psychologists regarding the study of human intelligence (Deary, 2001). Individual differences in several psychological attributes other than intelligence are critical for understanding the behaviour of people. In the past forty years there has been growing interest in the role of these individual differences, because they appear to modulate human behaviour in important domains such as work, health, and education. Chess can provide a commensurate model of human behaviour, akin to the Drosophila model in the biological sciences (Simon & Chase, 1973). Chess has typically been used in terms of the experimental approach to model several theories concerned with cognitive psychology topics. Moreover, the studies carried out in the domain of chess have also increasingly suggested that there are individual differences in several human behavioural attributes, such as brain functioning, memory, thinking, decision-making, intellectual human performance, personality, and motivation. This book compiles and describes this latter body of research.

1.1 A Very Brief Opening to the Game of Chess The origins of the game of chess can be traced back to ancient India around the sixth century AD. Chess travelled first to the West, then, later, to the rest of the world. Nowadays chess has become the universal intellectual game par excellence, practised by millions of individuals of diverse nationalities, ages, and backgrounds. Chess is played on an eight by eight squared board, divided into thirty-two light squares and thirty-two dark squares. Each square is uniquely 1

2

introduction

Table 1.1 Overview of the two main approaches to psychological research

Aim

Unit of analysis Hypotheses Research design Data analyses

Validity

(a)

Experimental

Correlational

Functional analyses of psychological processes Cognitive processes Inference Experimental

Analysis of individual differences and regularities in behaviour

ANOVA ANCOVA MANOVA Internal

Psychological traits Covariation Ex-post-facto Probabilistic Correlation Factor analysis Causal analyses External

(b)

Figure 1.1 A chess game with all intervening pieces in action (left diagram); a chess problem with white to play and win (right diagram; taken from a game between Velmirovic and Csom in Amsterdam, 1974)

identified by a coordinate system using Latin letters from a to h and numbers from 1 to 8. This board imitates a battlefield on which two armies, one black and one white, confront each other in a merciless fight. Each of the two armies comprises eight pawns, two rooks (R), two knights (N), two bishops (B), a queen (Q), and a king (K). The left diagram in Figure 1.1 shows an ongoing typical chess clash with all these intervening pieces. The specific moves of all pieces are described briefly in the Glossary, together with the value of each piece, indicated by the points usually assigned to it. The aim of the game

a very brief opening to the game of chess

3

consists in checkmating the opponent’s king. The army that first checkmates the enemy king wins. The basic rules of the game are very simple and very easy to learn, even at younger ages and at any educational level. Yet the game as a whole becomes extremely complex. There are literally several millions of millions of different combinations among the contending pieces in a single chess game. These combinations can be represented with a chess tree, an informational device in which the solution is the path leading to victory. A chess tree typically generates a massive and unmanageable amount of combinations (10120) even for the most powerful and fastest computer chess engines, let alone for human beings (Shannon, 1950). Because each of the pieces involved in the game obeys different movements, the game is intellectually demanding, while requiring the interplay of a variety of major psychological attributes and processes, such as perception, memory, reasoning, decision-making, problem solving, will, motivation, interests, and creativity. Consider, for instance, the right diagram in Figure 1.1. This represents a typical chess problem with the white forces to play and win. There is an efficient sequence leading to the white victory that comprises five precise moves, with an average time limit to solve it of about ten minutes. The correct sequence of moves in algebraic notation is shown below, for both white and black pieces:

1 2 3 4 5

White

Black

B×f7+ Q×e8+ R×e8+ d7 Rf1!!

R×f7 N×e8 Rf8 Qd6 1–0

Each of the five chess moves comprise two plies: one ply for white, and one ply for black. The ply corresponding to black in the fifth move indicates that white has won the game (scoring one point), however, because, after the last ply of white (Rf1), there is no possible legal move by black to avoid being checkmated at the very next move by white. Capital letters stand for the specific chess piece being moved and the × symbol indicates that a piece captures an opponent’s piece. For instance, the first ply for white (B×f7+) indicates that the white bishop (B), initially placed in the b3 square, is capturing the pawn located in the f7 square. The + symbol indicates that the black king is placed in check. A ply depicting a single square only indicates a pawn move. For instance, the fourth ply for white (d7) indicates that the pawn placed in the square d6 advances to the square d7. The double exclamation mark in the fifth

4

introduction

ply for white (Rf1!!) indicates a brilliant and very strong move. In this specific game, it was a coup de grâce move, winning the game. People may differ greatly in terms of their chances of finding out this sequence of moves. If you are a proficient chess player at the master level, you may be able to ‘see’ the sequence at a glance. It could also be the case that you may remember this position because you have already studied it in the past, during your long chess career. On the other hand, if you are a typical club chess player with a moderate level of chess skill, you might invest the suggested amount of time, but you may end up unable to figure out what the correct solution is at all. If you are a beginner chess player, or you just know the basic chess rules, the likelihood of experiencing serious difficulties in finding the solution may be so great as to be insurmountable. This is a very basic example of individual differences in chess performance and chess skill.

1.2 Overview of This Book Nowadays there is a considerable volume of chess studies that have highlighted noteworthy individual differences. For example, some of these chess studies use problems such as that shown in Figure 1.1 as experimental stimuli. This book is an attempt to compile and summarize the latest research about the psychology of chess with a focus on individual differences. Besides, this volume aims to provide an overview of the findings from more than forty years of research, from the mid-1970s to date, about chess and individual differences. This body of research has sometimes yielded inconclusive and even controversial results, suggesting, for instance, that the development of chess skill over time may largely depend on the combination of individual differences in several traits or broad clusters of traits. This book organizes the body of knowledge that uses chess as a model environment, while providing useful scientific information about a variety of individual differences in brain functioning, intelligence, personality, expertise, and sex, and in applied fields such as business, health, and education. The book is mainly aimed at scholars within the broad spectrum of the social and behavioural sciences who have an interest in the psychology of chess. The book can be of interest to psychologists, sociologists, educators, neuroscientists, and behavioural scientists in general. The chapters are intended to cover the topics typically addressed by social scientists interested in individual differences working in a diversity of fields. Those researchers and academics working in brain functioning, human abilities, and personality may find the book appealing. Moreover, the book may also arouse the curiosity of researchers and academics working with topics such as expertise, sex differences, and education, or with a focus on applied fields. In addition, the book may also be of interest for people who play chess themselves. In particular, chess players wishing to gain a more in-depth understanding of the scientific

overview of this book

5

work undertaken with chess as a model domain from a psychological approach may find some stimulating information within these pages. Chapter 2 describes the Elo chess rating. What makes chess an optimum field for the study of individual differences is the availability of this objective quantitative measure to gauge a player’s chess strength. The Elo rating system is by far the most popular and accepted indicator worldwide for quantifying accurately individual differences in chess skill. Every chess player participating regularly in rated chess tournaments holds an Elo rating. The Elo rating changes according to the outcomes of the games played within a given time period, while considering the Elo rating of the opponents. The chapter describes how the Elo ratings of thousands of chess players are kept and periodically updated. It also outlines the updating mechanisms and some basic statistics of the Elo rating. In addition, the chapter describes some recent alternatives to rating chess skill, such as the Universal Rating System (URS). Appendix 1 summarizes the studies that have used the Elo rating as related to a variety of human behaviours. Chapters 3 and 4 provide an overview of the main findings from the cognitive and the individual differences approach to the psychology of chess, respectively. Chapter 3 reviews the main research findings from the cognitive or experimental paradigm within psychology, which originated with the precursor scientific works about the psychology of chess. Three main basic facets of human behaviour have been addressed within this general approach: perception, memory, and thinking. The main conclusions from this extensive body of research can be summarized by emphasizing the role of individual differences. Chapter 4 outlines the main tenets and constructs of differential psychology, the discipline that studies individual differences in behaviour relevant for central social realms such as health, education, and work. The chapter is structured around three main themes. First, it describes the characterization and appraisal of individual differences. Second, the PPIK theory is suggested as an optimal starting point to conceptualize and examine individual differences. This framework comprises traits from four broad dimensions: intelligence as process, personality, interests, and intelligence as knowledge. Third, the chapter closes by addressing the old but compelling debate about the heredity versus environment dichotomy in explaining complex human intellectual behaviour. Chapter 5 describes the studies addressing human biological factors in chess, with a focus on psychophysiology and brain imaging. Human psychophysiology is a multi-faceted and complex phenomenon. The game of chess has provided a proper domain for the study of the central psychophysiological mechanisms underlying psychological processes such as stress, emotion evaluation, and decision-making. Moreover, novel technologies designed to provide high-resolution brain imaging are being increasingly used to explain human behaviour. These technologies have also been used with chess players to

6

introduction

examine the interrelationships of brain and cognitive functioning, and with personality and intelligence factors. In particular, this chapter outlines the research undertaken with electroencephalography (EEG), functional magnetic resonance imaging (fMRI), and positron emission tomography (PET). The chapter summarizes this body of evidence while underlining the most significant conclusions that may be derived from this intriguing and thoughtprovoking field of research. Chapter 6 provides an account of the studies addressing chess and intelligence. Human intelligence is one of the main general objects of study in individual differences research. There are indeed multiple models about and approaches to human intelligence, which are briefly described within this chapter. Chess has been typically associated with a high level of intelligence. Whether chess players are more intelligent on average than the general population is a recurrent question that has elicited a considerable body of research. There are unsettled issues as to what constitute the most advantageous cognitive abilities required in chess, and whether playing chess makes people smarter. These topics have been addressed with both children and adults. The scientific evidence in connection with this topic is inconclusive, however, and controversial in some instances. This chapter addresses these matters of contention by summarizing the state of the art in this particularly cogent field of research. The final section in the chapter includes novel empirical findings comparing chess skill and chess motivation in the prediction of chess performance, suggesting that non-cognitive traits might also be influential for chess performance. Chapter 7 analyses what is already known about chess and human personality. Personality is the other main broad domain addressed within the general framework of individual differences. In contrast with intelligence, however, the body of research concerning the personality of chess players is rather scarce. There have been some interesting findings recently, however, and these are summarized within this chapter. After describing briefly the main approaches to addressing human personality, some questions addressed in this chapter are whether personality influences chess playing style, or whether a chess player’s personality differs in some special way from that of other people. In addition, whether personality factors may interact with cognitive abilities in chess players is an interesting and relatively novel topic. The chapter closes by presenting novel data about the interplay between personality, motivation, and emotional regulation in predicting chess skill. Chapter 8 analyses expertise, one of the most prolific fields in empirical research using chess as a model domain. Expertise is of great importance in several realms of human intellectual activity. The role of practice in the development of chess expertise is reviewed in detail in this chapter. Moreover, the role of practice is contrasted with talent, because the deliberate practice approach has advanced the idea that expert performance depends

overview of this book

7

exclusively on practice. A consistent body of evidence suggests that deliberate practice alone is unable to explain the individual variability in chess expertise, however. The present chapter addresses this controversy by framing these findings in the nature versus nurture debate, one of the central themes within individual differences research. Furthermore, this chapter also explores agerelated cognitive decline in human intellectual activity, which appears to occur to a lesser extent in the chess domain. For instance, recent findings suggest in particular two interrelated factors that may be highly relevant in preventing cognitive decline in chess: the level of expertise attained, and the amount of tournament activity. Chapter 9 tackles the issue of sex differences in chess. On average, men tend to start earlier, perform at a higher level, and persist longer than women in the chess domain. Moreover, women are highly underrepresented in chess, which is also apparent in several other domains, such as those connected with STEM fields (science, technology, engineering, and mathematics). The marked difference in the number of men and women participating in chess has led to the assumption that the differences in chess performance between men and women are attributable to a statistical effect derived from the differences in participation rates. In contrast, other findings suggest that men might have an innate advantage in terms of chess playing, enhanced by certain cultural factors. These two points of view are addressed in this chapter. The alternative explanation to the marked disparity in chess participation and performance between the two sexes may be related to the participation of men and women in STEM fields. In addition, there are some noticeable differences in the chess playing of men and women, even though women are able to play very strong chess, just like men. The chapter closes by presenting a statistical analysis with data from the chess domain, which relates to sex differences in performance at different levels of practice. The findings from this analysis suggest that sex differences in the Elo ratings tend to increase with increasing practice, pointing to factors other than practice as the underlying causes of these sex differences. Chapter 10 deals with the applications of chess in three major fields of human activity: business, health, and education. Chess has been used in the business field with two main aims. First, chess has been used for educational purposes to teach and consolidate concepts connected with this discipline. Second, some studies have used chess as a model to evaluate game-theory aspects of the game. The game of chess has also been increasingly used to address health-related problems such as attention deficit hyperactivity disorder (ADHD), neurodegenerative disorders, and schizophrenia. Moreover, chess has become an increasingly popular pedagogical method in several school settings across the world. A number of studies claim that chess training entails several educational benefits for core academic subjects such as languages and mathematics, and also for concentration and self-control, or the development of socio-affective competences. Several of the instructional experiences that use chess to enhance these

8

introduction

behaviours are described in this chapter. Some recent studies suggest that significantly higher levels of academic performance for schoolchildren and adolescents are associated with chess-based teaching or the practice of chess on a regular basis, when compared with those students who are not involved in chess playing or chess instruction. Another set of studies have questioned the purported benefits of chess training for formal education, however. From this latter point of view, there are both conceptual and methodological concerns that compromise to a great extent the available evidence about the association of chess training with academic achievement. Two of these issues relate to the transfer of abilities across domains, and to the concept of statistical power. Chapter 11 is the closing chapter of this book. This chapter argues why chess has become an interesting domain to address topics of interest for individual differences research. It also summarizes the most robust available evidence to date by outlining the key findings, while suggesting some tentative and potentially promising steps for advancing the field.

2 Quantifying Chess Skill

What makes chess an optimum field for the study of individual differences is the availability of an objective quantitative measure of a player’s chess strength. This is an important asset compared with other applied domains, because they lack such a systematic indicator of skill. Although several indicators quantify accurately chess skill, the Elo rating system is the more popular chess skill indicator, accepted worldwide. For example, the Elo rating system is useful in the organization of formal chess tournaments, such as in pairing players of equivalent chess strength, or in restricting participation in chess tournaments to a given chess strength level or to groupings of players with different levels of chess skill. Because the Elo rating is an interval scale, it lacks a true zero, though it allows the quantification of an objective difference between each value. Every chess player participating regularly in rated tournaments holds an Elo rating. The Elo rating is a dynamic indicator that depends on the outcomes of the games played within a given time period, taking into account the Elo rating of the opponents. Such a system has been deemed highly appropriate to track changes in the variability of its scale values, which might be useful for addressing an extensive variety of research problems within differential psychology or individual differences research (Batchelder & Bershad, 1979; Howard, 2006). A sense of the variability in chess skill as measured by the Elo rating can be gleaned by looking at the world maps displayed within Appendix 2. These maps represent data for 118 countries obtained from the December 2018 list of the World Chess Federation (Fédération Internationale des Échecs, FIDE). The first map shows the mean Elo rating, and the second map shows the number of chess grandmasters by country. There are only three countries with a mean Elo rating above 2700 Elo points – Russia, China, and the United States – and twelve countries with a mean Elo rating above 2600 Elo points: Azerbaijan, Ukraine, India, France, Armenia, Hungary, the Netherlands, Poland, the United Kingdom, Israel, Germany, and Spain. Cross-country differences are more pronounced, however, when looking at the number of grandmasters in the second map. Here, Russia holds a noteworthy advantage over the rest of the countries, with 251 grandmasters, in front of the United States, with ninety-eight, Germany, with ninety-six, and Ukraine, with 9

10

quantifying chess skill

ninety-one. There is then a group of five countries with between fifty and fifty-seven grandmasters: Serbia, Hungary, India, Spain, and France. In contrast, the world regions with the lower mean Elo ratings and number of grandmasters correspond to Africa, and several countries in Central and South America, and Asia. The two maps evidence the universality of the game, which is surely unparalleled by any other game of its kind.

2.1 Elo Rating Lists The systematic updated records of the Elo ratings of chess players from all over the world allow the study of individual differences in intellectual performance from an objective point of view. Every chess player participating regularly in rated chess tournaments of any kind holds an Elo rating that ranges from approximately 1,200 to about 2,850 points, with higher scores being indicative of a higher level of chess strength (Elo, 1978; Glickman, 1995; Glickman & Chabris, 1996; Glickman & Jones, 1999). Chess federations worldwide keep and update periodic records of the Elo ratings of their respective players. In addition, players participating in international tournaments hold the Elo rating of the respective player’s country or local chess federation, and the international Elo rating assigned by the World Chess Federation (Fédération Internationale des Échecs: FIDE). Elo ratings from different chess federations tend to be highly correlated. There are even Elo rating lists from a variety of computer chess engines. Figure 2.1 shows part of the Elo rating lists of the FIDE, the Spanish Chess Federation, and the Catalan Chess Federation, and the Elo ratings of 353 computer chess engines. The lists from the World and Catalan Chess Federations and from computer engines are ordered by the rank of the strongest players. The World Chess Federation list shows the ten strongest players. The Catalan Chess Federation list indicates the chess title and sex of each player (GM: Grandmaster; M: Male). The computer list shows the number of games played and the percentage of winning outcomes. The Spanish Chess Federation list is in alphabetical order by the player’s surname, and it also includes the number of games played in the given period, the year of birth, the title, whether the player is active or inactive (A, I), and the previous Elo rating. For instance, the current Elo of the first player in this list is 1851 points, while his previous Elo was 1842. Therefore, the player has gained nine Elo points in this latter Elo update. In contrast, the player with Id. FEDA #26 has a current Elo of 2177, while his previous Elo was 2181. Therefore, this player has lost four Elo points in this latter Elo update.

updating mechanism of the elo rating (a)

(b)

(c)

(d)

11

Figure 2.1 Elo rating lists of the World (a), Spanish (b), and Catalan Chess Federations (c), and Elo rating list of top twenty-eight computer chess engines out of a list of 353 engines (d)

2.2 Updating Mechanism and Basic Statistics of the Elo Rating The Elo rating is a dynamic indicator that depends on the outcomes of the games played within a given period considering also the Elo ratings of the opponents. To illustrate, the elements implied in the calculation and updating

12

quantifying chess skill

of the Elo rating after the outcome of a chess game between two players can be described in three main steps (Elo, 1978; Glickman, 1995): 1. There are three possible outcomes arising from a chess game: win = 1, draw = 0.5, defeat = 0. 2. The expected score (E) in a chess game between players A and B with ratings RA and RB can be calculated for player A with the expression in Equation 2.1: E¼

10RA =400 10RA =400 þ 10RB =400

ð1Þ

3. The update of the Elo rating is calculated with the expression in Equation 2.2. This includes a previous Elo rating (rpre), the Elo rating after a chess tournament (rpost), a constant value (K), the sum of points obtained in the tournament (S), and the sum of expected scores in each game (Sexp): rpost ¼ rpre þ K ðS  Sexp Þ

ð2Þ

In a single chess game, a win scores one point, a defeat scores zero points, and a draw scores half a point. The expression in Equation 2.1 can be conceived as the actual probability of winning a chess game considering the Elo rating of both opponents. The Elo rating is indeed an accurate predictor of the outcome of a chess game. A stronger player in terms of a higher Elo rating has increased chances of scoring one point when playing against a weaker player. In contrast, a weaker player in terms of a lower Elo rating sees his or her chances of scoring one point greatly decreased when playing against a stronger player. The expression in Equation 2.2 serves to update the Elo rating in accordance with the performance of a player within a given period. The new and updated Elo rating (rpost) is calculated by summing the observed previous Elo rating (rpre) and the term K(S – Sexp). The value of K corresponds to an attenuation factor that represents the amount of weight allotted to a new Elo rating given an old Elo rating – that is, the maximum number of points that increase or decrease the rating from the outcome of a single chess game. Larger K values allow greater changes in Elo ratings. Usually, younger and less experienced players tend to have higher attenuation K values than older and more experienced players. The value (S – Sexp) indicates the discrepancy observed between the actual points (S) obtained within a given period and the expected points (Sexp), calculated with the expression in Equation 2.1 in accordance with the Elo ratings of the corresponding opponents in the chess games played within this period. Positive values in (S – Sexp) indicate that the player performed above what was expected, whereas negative values indicate that the player

updating mechanism of the elo rating

13

Table 2.1 Example of the Elo rating updating in one chess game between players KS versus AB, and JP versus LQ

Player Elo rating K

Game Expected score Actual score outcome

Elo update

KS AB KS AB KS AB JP LQ JP LQ JP LQ

0.97 0.03 0.97 0.03 0.97 0.03 0.44 0.56 0.44 0.56 0.44 0.56

2544 1935 2534 1951 2539 1943 2071 2098 2056 2113 2065 2105

2544 1936 2544 1936 2544 1936 2064 2106 2064 2106 2064 2106

10 15 10 15 10 15 15 15 15 15 15 15

1 0 0 1 0.5 0.5 1 0 0 1 0.5 0.5

Win Defeat Defeat Win Draw Draw Win Defeat Defeat Win Draw Draw

performed below what was expected. Therefore, the updated Elo rating will increase or decrease accordingly. Table 2.1 shows two examples of the Elo rating update in a hypothetical chess game. In the first example, concerning players KS and AB, there is a considerable difference between the Elo ratings of the two players, 608 points, while player KS holds a lower K value of ten compared with the K value of fifteen for player AB. The first two rows in the table show the most likely situation after the game: a victory of the player with the higher Elo rating. The Elo rating update for this player would be unmodified from the previous Elo rating (Elo update = 2544). On the other hand, the Elo rating for player AB would decrease the previous Elo rating (Elo update = 1935) by just one point. In contrast, with an unlikely defeat of the stronger player, KS, the previous Elo rating decreases by ten points (Elo update = 2534), while for the weaker player, AB, there is an increment of fifteen points (Elo update = 1951). The result of a draw, with 0.5 points for each player, is also more advantageous for the weaker player; it decreases the Elo rating of KS by five points (Elo update = 2539), while increasing the Elo rating of AB by seven points (Elo update = 1943). In the second example, the difference between players JP and LQ is only forty-two Elo points, which is markedly lower than in the previous example, with both players holding a K value of fifteen. The three possible outcomes of the game, win, draw, and defeat, indicate a more balanced outcome for each player concerning their corresponding Elo updates. This is perhaps better seen

Density

quantifying chess skill 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014

14

500

1000

1500

2000

2500

3000

Elo rating

Figure 2.2 Density plot of the Elo rating with normal (continuous line) and logistic (dotted line) distributions

in the last two rows, which describe the draw situation, which modifies the Elo update by just one point for each player. The Elo rating system can be framed within the Bradley–Terry model for predicting the comparison of a pair of objects or individuals (Bradley & Terry, 1952), albeit, in its development, the Elo rating system assumed a normal distribution. Nevertheless, the Bradley–Terry model relies instead on logistic distribution assumptions, which is the approach taken by the World and the US Chess Federations (Glickman, 1995). Figure 2.2 shows both normal and logistic probability distributions for a simulated sample of 1,000 players with a mean of 1700 Elo points (Sd = 200). There are higher density estimates at the centre of the normal distribution, and longer extended tails for the logistic distribution. On the other hand, Figure 2.3 shows the density plots from four different chess tournaments in four variables: the age of the participants, the number of games prior to the tournament, the tournament outcome, and the Elo rating. The data corresponding to the four tournaments indicate a relatively consistent overlap apart from for the Elo rating, suggesting that the Elo rating was more variable than age, number of games, or tournament

alternatives to the elo rating of chess players

Density

0.000

0.01 0.00

0

−50 0

20 40 60 80 Age of participants

50 150 250 Number of games

0.0000

Density

0.10 0.00

0 2 4 6 8 Tournament outcome

0.0010

(d) 0.20

(c)

Density

0.004

0.008

0.04

(b)

Density 0.02 0.03

(a)

15

1200

1600 2000 Elo rating

2400

Figure 2.3 Density plots for the distribution of the Elo ratings in the age of participants (a), number of games (b), tournament outcome (c), and Elo rating (d) of four chess tournaments

outcomes. Table 2.2 displays the descriptive statistics in the Elo rating across the four chess tournaments. The Shapiro–Wilk normality tests for the Elo rating in the four tournaments suggest that the null hypothesis stating that the sample comes from a population with a normal distribution is unsupported by these data.

2.3 Alternatives to the Elo Rating of Chess Players The Elo rating system has gained considerable acceptance and has been used worldwide for over forty years since its inception (Elo, 1978). There are several criticisms and suggestions for improvement, however. For example, it has been recommended that chess ratings should deal with unrated and recently rated players, and that the K attenuation factor should be related to the number of

16

quantifying chess skill

Table 2.2 Descriptive statistics of the Elo ratings in four chess tournaments Statistic

Tournament 1

Tournament 2

Tournament 3

Tournament 4

n Min Q1 Q2 Q3 Max M Sd Cv Skewness Kurtosis W

107 1873 2034 2234 2411 2625 2234 213 0.10 0.01 -1.27 0.95***

100 1200 1591 1878 2143 2574 1847 386 0.21 -0.15 -0.80 0.96**

85 1200 1724 1982 2349 2596 1975 393 0.20 -0.32 -0.73 0.95**

81 1200 2025 2131 2394 2577 2165 262 0.12 -1.03 2.86 0.91***

Notes: n = sample size; Min: minimum; Q1 to Q3: quartiles 1 to 3; Max: maximum; M: mean; Sd: standard deviation; Cv: coefficient of variation (Sd/M); W: Shapiro–Wilk normality test (H0: the variable follows a normal distribution); **p < 0.01; ***p < 0.001.

games played (Fenner, Levene, & Loizou, 2012). There are, in addition, other alternatives to rate chess skill by relying on Bayesian methods. For instance, there is a proposal to estimate chess skill from the moves played in an assortment of chess games, rather than from competitive chess outcomes (Di Fatta, McHaworth, & Regan, 2009). Other work has focused on the modelling of draws and the inference of chess skill from chess team outcomes (Herbrich & Graepel, 2006). Furthermore, there are other approaches raising substantial modifications to the Elo rating system. For example, Chessmetrics is a comprehensive internet database about the rating of the chess skill of chess masters throughout history. Jeff Sonas, the developer and chief engineer of Chessmetrics, proposed an alternative system to calibrate chess skill with alternative methods to the Elo rating (Sonas, 2002). There were four main suggestions regarding the Sonas system: using a more dynamic K-factor; dismissing the Elo table and opting for a simpler linear model; including faster time controls, albeit assigning them a lower importance than slower time controls; and calculating the chess ratings on a monthly basis. Moreover, other alternative chess rating systems include the Glicko (Glickman, 1999), the Glicko-2 (Glickman, 2001), and the Universal Rating System (URS), all of them developed by Professor Mark Glickman, a statistician at Harvard University, together with other researchers.

overview of studies using the elo rating

17

The URS is a particularly appealing system, because it provides a single rating for each individual obtained from the outcomes of games played at different time controls. In the FIDE Elo rating system, chess players can have up to three different Elo ratings stored in three different lists: standard, rapid, and blitz ratings. The three ratings are highly correlated (r > 0.90). The standard Elo rating is estimated from the outcomes obtained in standard slow games, which allow at least two hours for each player for their first sixty moves. The rapid Elo rating is estimated from the outcomes obtained in fast games that last more than ten minutes but less than sixty minutes for each player. The blitz Elo rating is estimated from the outcomes obtained in very fast games, which last ten minutes or less for each player. Faster blitz games, therefore, impose serious constraints on the available thinking time, whereas slower standard games allow for a larger amount of thinking time. This fact has been capitalized on for analysing chess thinking strategies such as pattern recognition and search A lower amount of available thinking time is likely to foster a more intensive application of fast pattern recognition, whereas a higher amount of available thinking time is likely to foster a more intensive application of slow search thinking (Burns, 2004; van Harreveld, Wagenmaapplication of slow search thinking (Burns, 2004; van Harreveld, Wagenmakers, & van der Maas, 2007). The URS contemplates the variability of the outcomes in chess games from five minutes (blitz) to two hours (standard), by calculating the degradation of playing skill from slower to faster games. The degradation from slower to faster games is indicated with rapid or blitz gaps with respect to slower games, with higher values being indicative of a higher degradation. Even though they use information from the outcomes in games at different time controls, the designers of the system acknowledge the lower informative value of faster games compared with slower games about the true underlying individual chess skill. Thus, fast game outcomes contribute to the URS to a lesser extent than slow game outcomes. A detailed description of the URS is available through the internet at http://universalrating.com.

2.4 Overview of Studies Using the Elo Rating Because the aforementioned rating systems have only recently been implemented, most of the studies in the psychology of chess have addressed individual differences in chess performance by considering the Elo rating as a central variable of interest. The Elo rating is an appealing indicator that has attracted considerable attention from diverse fields of research. Elo rating data has been used to model animal and macroeconomic behaviour (Albers & de Vries, 2001; Burns, 2004), computerized adaptive testing (Moul & Nye, 2009), and evolutionary algorithms within computing science (Antal, 2013). For instance, a statistical study has addressed three interesting hypotheses (Breznik & Batagelj, 2011): (1) whether the best players in the world tended to

18

quantifying chess skill

play exclusively among themselves; (2) whether the amount of games played depended on geographical proximity between countries; and (3) whether the advantage of conducting the white pieces should be considered in determining the strength of a chess player. The analyses were based on an extensive sample of chess players (n = 92,731) with one of the FIDE Elo rating lists. The findings in the study support the view that the best players were quite selective concerning chess tournaments. Besides, chess players from different countries played each other more often when they came from neighbouring countries. Finally, conducting the white pieces was judged as an important advantage at higher levels of chess skill, suggesting that it should be also contemplated in the calculation of chess ratings. The Elo chess rating is a quantitative measure that allows the estimation of individual differences in chess skill accurately and reliably, and it has been extensively used in the research about individual differences in the chess domain. Appendix 1 shows a representative overview of the studies about human behaviour that have used the Elo chess rating or analogous ratings from diverse chess federations, and the factors potentially related to these measures of chess skill (n = 134). For each study there is the journal in which it was published, the number of participants or sample sizes (N), and the main conclusions. In some studies, the Elo ratings were used to split a given sample of chess players into diverse levels of expertise, and, subsequently, to apply different batteries of psychological tests or experimental tasks. Other studies analysed the association of the Elo rating with a variety of outcomes, such as brain and psychophysiological activity, the quality of chess playing, perception, memory, reasoning, verbal and processing speed performance, intelligence, personality, sex and age differences, practice, expertise, and learning. In what remains of the present book, each of these themes will be addressed in depth, by delving into the main correlates of the Elo chess rating that have been found in this body of research.

3 Cognition

The cognitive approach to the psychology of chess encapsulates that branch of research interested in the mental processes elicited when playing chess, or when working with chess material within an experimental setting. Empirical studies conducted using this approach generally enquire about the mental processes implied in the intellectual activity of chess that are common to all individuals. That these processes might largely depend on individual differences in chess skill was readily envisaged in earlier studies within the field, however (Binet, 1893, 1894; Cleveland, 1907; de Groot, 1965; Djakow, Petrowski, & Rudik, 1927). These early works agreed fairly well about the main psychological factors implied in chess playing. For example, the foundational work by Alfred Binet addressed mental processes elicited during simultaneous blindfold chess playing, a stringent chess modality whereby one person plays several opponents without actually visualizing the boards (Binet, 1894). The performance in blindfold chess playing should be likely to depend on individual differences in knowledge and experience in the domain of chess, together with imagination, and memory. Other central psychological attributes highlighted as harnessing individual differences in chess playing were memory, accurate analysis, quickness of perception, constructive imagination, and far-sighted combinations of chess pieces (Cleveland, 1907). Furthermore, factors such as memory, attention, highlevel intellectual processes, imagination, will, and psychological type were the main psychological factors advanced as underlying chess talent (Djakow et al., 1927). The first fully comprehensive work about chess psychology, however, was that carried out by Adriaan de Groot, a psychologist and a proficient chess player and international master who represented the Netherlands in the Chess Olympiad (de Groot, 1965). Thought processes elicited in chess were studied by presenting chess players with positions from actual games while asking them to choose the correct move and think aloud the process to reach the given choice. One important finding in the work by de Groot was that grandmaster players showed a striking superiority in selecting the strongest moves in a chess position, compared with lower-level players who tended to select poorer 19

20

cognition

moves. Subsequent work has placed the focus on three main mental processes that are central in the domain of chess: perception, memory, and thinking.

3.1 Perception These days computers hold an enormous advantage in chess playing over human opponents. It has now been more than twenty years since the Deep Blue machine defeated world chess champion Garry Kasparov in an epic battle in 1997 (Campbell, Hoane, & Hsu, 2002). Specific advantages of machines over humans in chess playing encompass a higher short-term memory capacity, speediness in individual calculations, the avoidance of errors, and analysis of the position free from emotional and instinctive constraints (Berliner, 1974; Shannon, 1950). The design of the first computers capable of playing chess entailed human-like attributes such as perception, problem evaluation, and decision-making with regard to the most likely moves leading to a solution of a given chess problem (Scurrah & Wagner, 1970; Simon & Barenfeld, 1969). Machines base their chess strength, however, on an efficient search within the chess tree of valid continuations arising from a given position (see Figure 3.1), which readily becomes massive after a few moves from both players (Shannon,

Figure 3.1 The representation of a chess tree with 86 nodes begins in the black central node, which splits into three main variants (dotted lines); each successive node splits into three lower-level nodes, representing the alternative choices arising at each main variant

perception

21

1950). In searching within the chess tree, an important aim of original chess software was in fact to narrow the search in a meaningful way (Berliner, 1974). Modern chess-playing computers in the last two decades, from Deep Blue to Alpha Zero, have excelled in this kind of behaviour by implementing relatively novel algorithms, such as quiescence search, iterative deepening, transposition tables, principal variation, and deep neural networks (Campbell et al., 2002; Silver et al., 2018). Hence, chess engines are highly resourceful at thinking, heuristic problem solving, and searching more speedily and more deeply within the chess tree, while being able to defeat the strongest human players in the world. In contrast, humans appear to perceive the properties and particularities of a chess position without initially seeking the specific solution through the branches of the chess tree (Simon & Barenfeld, 1969). There is an interesting finding, which has been replicated in several studies (Vicente & de Groot, 1990). Human chess players are asked to reproduce a given chess position, with over twenty chess pieces, that has been seen beforehand for a relatively short time interval of between two and ten seconds. The accuracy in reproducing the given position is positively correlated with individual differences in the level of chess skill. When the task is repeated with the pieces placed randomly in meaningless chess positions, though, the correlation is still positive, albeit lower than with normal meaningful chess positions (Chase & Simon, 1973; Simon & Chase, 1973). It has been remarked, however, that the correlation might hardly be significant, because of the low sample and effect size, while stronger players may still perform better than weaker players (Gobet, 1998). This crucial finding highlights the importance of basic perceptual processes in explaining the overwhelming advantage of stronger players over weaker players when solving a chess problem or judging a chess position. From this viewpoint, even though the structure of the search process might be very similar across chess players of varying strength, there will be differences in the possible paths suggested by the chunks stored in long-term memory (Simon & Chase, 1973). Indeed, when recalling a random distribution of pieces, chess players with higher levels of chess skill still perform better than chess players with lower levels of chess skill (Gobet & Waters, 2003; Goldin, 1979). Furthermore, recall performance in terms of random positions may also depend on the convergence of the pieces on the same squares. Chess masters showed better recall performance than class A and class C chess players when the chess pieces were located in the central squares rather than in the peripheral squares of the board (Reynolds, 1982). In addition, it has been reported that stronger chess players are also faster in recalling chess positions, even though the variability in response time across normal and random positions is unrelated to chess skill (Saariluoma, 1985).

22

cognition

Information-processing models have been used extensively to address the perceptual processes of chess information (Chase & Simon, 1973; Simon & Barenfeld, 1969; Simon & Chase, 1973; Simon & Gilmartin, 1973). Table 3.1 shows some of these information-processing models. For instance, the MATER model was designed to detect significant relationships between the pieces and squares in a given chess position when searching for a checkmate continuation (heuristic search). The PERCEIVER model was designed to gather information about the relationships among the pieces and squares in a chess position (information gathering). The combination of EPAM with MAPP accounts for the perceptual human processes used to remember and reproduce chess positions after examining them during a short time interval. The CHREST model, based on PERCEIVER and MAPP, considers four components and four main mechanisms: eye movements, information encoding and storing into long-term memory, learning from long-term memory, and information updating in the mind’s eye component (Gobet & Simon, 2000; Waters & Gobet, 2008). Table 3.1 Information-processing models to explain perceptual processes in chess (EPAM = elementary perceiver and memorizer; MAPP = memory-aided pattern perceiver) Model

References

Main goal

Postulates/components

MATER

(Simon & Chase, 1973)

Search for checkmate continuations.

Humans use information from a position and apply heuristic rules to select a reduced set of potential solutions for further consideration. Gather information about meaningful relations between chess pieces related to chess rules, such as defending and attacking.

PERCEIVER (Simon & Simulate human eye Barenfeld, movements. 1969; Simon & Chase, 1973)

perception

23

Table 3.1 Cont. Model

References

EPAM

(Simon & Store tests of chessboard There is a single learning Chase, 1973; locations in a binary process and a single Simon & tree structure. The resulting chunk. The Gilmartin, terminal nodes of the time needed to fulfil 1973) tree (leaves) store a given learning task is specific known patproportional to the terns of chess pieces. amount of chunks used in completing the task. (Simon & Simulate the human This model comprises Chase, 1973; processes to rememlearning and perSimon & ber and reproduce formance compoGilmartin, chess positions that nents. The learning 1973) have been seen briefly. component uses the mechanism of EPAM; the performance component uses the mechanisms of PERCEIVER and EPAM. (Gobet & Model learning and This model comprises Simon, expertise. four modules: 2000) a simulated eye, a discrimination network that gives access to long-term memory, a short-term memory, and a mind’s eye.

MAPP

CHREST

Main goal

Postulates/components

The exploration of eye movements constitutes another central line of research addressing the visualization of chess positions and chess playing. Initial work on this topic investigated chess master’s impressive efficiency in grasping the significance of a chess position. More skilled players might fix their eyes on the most salient pieces of the position, encode two or more chess pieces in a single eye fixation, cover larger chessboard areas – in sum, perceiving groups of pieces as single meaningful information units (de Groot, Gobet, & Jongman, 1996; Tikhomirov & Poznyanskaya, 1966). Further empirical

24

cognition

studies have also indicated superior perceptual ability on the part of expert over non-expert chess players. Stronger expert players appear to make fewer eye fixations, albeit greater-amplitude saccades, than intermediate players. In addition, stronger players fix their eyes more frequently on empty chessboard squares and on the most relevant pieces that conform to a particular chess position. These findings suggest that, rather than encoding individual pieces, expert players have an advantage in encoding chess configurations or broad patterns incorporating several chess pieces (Charness et al., 2001). Expert chess players also tend to invest more time in studying the relevant squares for familiar solutions than the relevant squares for the optimal solution. These findings have been interpreted as supportive of the Einstellung effect, whereby one fixed idea prevents other ideas coming to mind (Bilalić, McLeod, & Gobet, 2008b). The combination of the analysis of eye movements with the recording of brain activity has confirmed the remarkable advantage of experts over nonexperts. This advantage relates to the more extensive knowledge base of diverse chess patterns. For example, studies applying the electroencephalography technique indicate that the chess players who are more proficient at attending to the relevant parts of the position present more brain activation in areas related to planning and decision-making, such as the prefrontal cortex. In contrast, chess players who are less proficient fix their eyes on larger spaces, which requires the processing of a larger amount of information. These players show more brain activation in areas related to the processing of visual stimuli, such as the occipital and parietal cortex (Silva-Junior et al., 2018). Moreover, findings from fMRI studies have indicated that chess experts are able to recognize a given meaningful chess position while ignoring trivial configurations quickly and efficiently, although this ability decreases with random patterns of meaningless chess positions (Bilalić, Kiesel, et al., 2011; Bilalić et al., 2010, 2012). On the other hand, it has been suggested that the higher perceptual encoding ability of expert chess players might also depend on their higher chess experience and knowledge, rather than on a general perceptual or memory superiority (Kiesel et al., 2009; Reingold et al., 2001). From this viewpoint, the superior recall skills of expert over novice chess players for briefly presented chess positions are associated with the intrinsic disposition of the pieces on the board – i.e., the geometry, form, and colours of the chessboard and pieces, and the greater familiarity of experts with meaningful dispositions of chess pieces (Bilalić, McLeod, & Gobet, 2009; Schneider et al., 1993). For example, an interesting study in this line of research adopts the diametrical terms of ‘underdeveloped’ or ‘developed’ chess patterns (Ferrari, Didierjean, & Marmèche, 2008). Underdeveloped chess patterns correspond to chess positions whereby the pieces are located in the chessboard rows 1, 2, 7, and 8, which may bear a lower strategic value. Developed patterns correspond

memory

25

to chess positions whereby the pieces are located in the chessboard rows 3, 4, 5, and 6, which may bear a greater strategic value. Ferrari and collaborators examined whether experienced players would be faster at encoding underdeveloped than developed patterns with a flicker paradigm and a recognition task in a two-experiment study. As expected, the findings indicate that more experienced players are faster at encoding developed patterns than at encoding underdeveloped patterns (three to four seconds), whereas novice players are slower (four to ten seconds) and invest an analogous amount of time in encoding both kinds of patterns. Expert players encode underdeveloped patterns – i.e., strategically unimportant ones – in a global and quick manner that allow them to focus instead on the strategically important developed patterns. Such a general strategy would be likely to allow for a more efficient application of analytical skills, which are, in turn, highly dependent on memory skills. Indeed, one of the fundamental elements during eye movements is visuospatial working memory (van der Stigchel & Hollingworth, 2018). The main target is selected before a saccade by the actual available content in visual working memory, supporting the view that perceptual and mnemonic processes intertwine closely in chess.

3.2 Memory Memory is a central attribute in chess playing. Once the flavour of a given chess position or problem has been captured through perceptual processes, a representation in both short-term and long-term memory occurs (Gobet & Simon, 1996a, 1996c, 1998a; Goldin, 1978, 1979). Because of the inherent limitations of human memory when confronted with an increased amount of information, the memorization of chess positions and combinations can be extremely taxing on account of the high density of the chess tree (Figure 3.1). Hence, individual differences in mnemonic abilities are likely to relate strongly to individual differences in chess performance (Baddeley, Thomson, & Buchanan, 1975; Furley & Wood, 2016). The stronger chess players hold a remarkable advantage over weaker chess players in recognition and recall processes tapping mnemonic structures (Goldin, 1978, 1979). There are four main models that account for the role of expert memory in chess and other domains (Gobet, 1998): the chunking theory (Chase & Simon, 1973); the search, evaluation, and knowledge theory (Holding, 1985); the long-term working memory theory (Ericsson & Kintsch, 1995), and the template theory (Gobet & Simon, 1996c). Table 3.2 summarizes these models by describing their main tenets and suggested degree of supportive evidence across five main dimensions: early perception; short-term recall and long-term encoding; modality of representation; long-term organization; and learning. About half the empirical available data were unsupportive of

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Table 3.2 Overview of theories addressing the role of expert memory in chess (LTM = long-term memory; SEEK = search, evaluation, knowledge) with the degree of supportive and unsupportive evidence (Gobet, 1998) Theory

Reference

Main tenets

Supportive

Unsupportive

Chunks

(Chase & Simon, 1973)

92%

8%

SEEK

(Holding, 1985)

31%

54%

LTM-WM

(Ericsson & Kintsch, 1995)

38% (square) 62% (hierarchy)

46% (square) 15% (hierarchy)

Template

(Gobet & Simon, 1996c)

Chess positions are encoded in memory as larger units than isolated pieces, including the relationships between pieces and empty squares – so-called chunks. Chess skill relies on the collection of chunks stored in LTM, allowing the recognition of very specific patterns. The three main elements in expert memory are search, evaluation, and knowledge. Search and evaluation draw on a broad knowledge base accumulated through years of experience. Chess positions and moves are selected from the sequences generated within a given chess tree by integrating search, evaluation, and knowledge. Chess positions are recovered from the 64-square chessboard defining a hierarchical structure that relates the chess pieces to each other and to their respective locations. The hierarchical structure is represented and working memory, allowing an accurate analysis and evaluation. The three main elements in expert memory are a database of chunks, a knowledge base, and a connection of the chunks to the knowledge base. Templates are larger chunks specifying the location of several pieces, and slots, eventually accommodating additional pieces and their locations.

100%

–

memory

27

either the SEEK or LTM theories, while the chunking and template theories have received a higher degree of support from empirical data (Gobet, 1998). The chunking theory is intimately linked with the information-processing models described earlier in the previous section about perception (Chase & Simon, 1973; Simon & Barenfeld, 1969; Simon & Chase, 1973; Simon & Gilmartin, 1973). A chunk is a familiar recurrent grouping of chess pieces that holds a connected structure based on attack, defence, same colour, same piece, and proximity relations. Essentially, the advantage of experts over novices consists in recalling more chunks from long-term memory, around 50,000, but also of a larger size. Ten years is the common estimation of the time needed to learn such a huge amount of chess information (Gobet, 1998; Gobet & Simon, 1998a). A central proposition of the chunking theory is that there is a recognition process during the presentation of a given chess position. This process uses a discrimination net to locate specific chunks in long-term memory, which are subsequently indexed in short-term memory. In this view, individual differences in chess skill depend on recognizing chunks and evaluating the consequences of candidate moves (Gobet & Simon, 1998a). The template theory emerged from the need to link low-level to high-level knowledge. The former represents the perception and memory of chunks and the latter represents the comprehension of the peculiarities of a given chess position and the selection of candidate plans and moves (Gobet, 1998). This theory combines the concept of a chunk with that of retrieval structures (i.e., templates). A template is an extension of a chunk, which renders familiar chess positions commonly found in specific openings or strategic plans. As with the chunking theory, a discrimination net consisting of a set of nodes (i.e., a decision tree) recognizes a chunk stored in long-term memory by familiarization and discrimination mechanisms. Templates have fixed locations of chess pieces, but also variable chess piece positions (i.e., slots) that can accommodate additional pieces together with their respective structural relations (Gobet & Clarkson, 2004; Gobet & Simon, 1996c). In accordance with this framework, individual differences in chess skill depend on a large amount of chunks indexed by the discrimination net, a large knowledge base encoded as production and schemas, and a connection of chunks to the knowledge base. Moreover, the template theory explains well why stronger players are better than weaker players at recalling both normal chess positions with chess meaning and meaningless random positions. In sum, the skill of chess experts when recalling a huge amount of chess games evidences the variety of templates stored in long-term memory (Gobet & Simon, 2000; Gobet & Waters, 2003). Several empirical studies report the unrivalled chess memory of stronger players, supporting a robust positive association with individual differences in chess skill. For example, a study with three experiments highlights that memorizing chess positions is a clear function of chess skill (Frey & Adesman,

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1976). This study also emphasizes that chess players with a higher level of chess skill are able to find more semantic relationships between the pieces and chunks, and that this deeper level of processing enhances a better memory performance. Another study with a Brown–Peterson paradigm including four experiments examined the limits of short-term memory in two groups of chess players. These participants were classified in accordance with the ranking of the United States Chess Federation as advanced or class A players, and average or class C players (Charness, 1976). The participants had to recall chess diagrams after seeing them for five seconds. In the meantime, they had to perform other tasks. Even though class A and class C players stored chess information within the five available seconds irrespective of the interfering tasks, class A players retained between 10 and 15% more information than class C players. Moreover, stronger players might also determine long-term memory chunks of chess information from attack–defence relations among the pieces rather than by their location or proximity (McGregor & Howes, 2002). This kind of ability has been consistently linked to visual working memory during blindfold chess (Saariluoma & Kalakoski, 1997; Saariluoma et al., 2004), and with the quick selection of candidate moves and the capacity to store chess representations (Robbins et al., 1996). The usefulness of chess knowledge in memory was underlined in a comparison of the memory of children and adults. The immediate recall of chess positions of child chess experts was superior to that of adult chess novices. Conversely, the performance in the classical digit span memory test of child chess experts was inferior to that of adult chess novices (Chi, 1978). A study with a larger sample of forty children and forty adults from Germany replicated these findings consistently (Schneider et al., 1993). Expert players outperformed novice players because of their greater acquaintance with meaningful chunks of chess pieces, with the geometrical pattern of the chessboard, and with the forms and colours of chess pieces. Chess experts have also been shown to process information more comprehensively when compared with recreational or novice players in a face recognition paradigm (Boggan, Bartlett, & Krawczyk, 2012). These findings from an experimental study comparing expert (n = 27), recreational (n = 22), and novice chess players (n = 20) were partly attributed to an underlying chunking and template formation process, which was common to both face and chessboard processing. The chunking and template theories of expert memory have highlighted the importance of memory for chess skill. In contrast, another group of studies have emphasized in turn the importance of abstract domain knowledge, such as the encoding of a chess position in terms of the strategic and tactical basis. For example, the aforementioned study, suggesting a robust association of memory performance and chess skill (Frey & Adesman, 1976), points out that more skilled players are better able to find more semantic relationships in chess information. Similarly, another set of experiments presented the chess players

memory

29

with high-level descriptions of chess positions with sentences such as ‘Queen’s gambit declined exchange variation-type position. White is conducting a minority attack. Black has defensive resources and some prospect of a kingside attack’ (position 2). The recall of the chess positions improved when the description was presented before rather than after actually seeing them, which was deemed as supporting the view that high-level abstract knowledge is the main determinant of the ability to recall chess positions (Cooke et al., 1993). Further outcomes suggest that stronger players are better able to integrate familiar chess piece configurations into comprehensible schemes (Lane & Robertson, 1979), and that the quality of the best chess moves depends on evaluation rather than on recognition processes (Holding & Reynolds, 1982). Moreover, knowledge of the legal rules in chess exerts a more influential role than memory for chess positions at lower levels of expertise (Yoskowitz, 1991), suggesting that deeper levels of processing contribute to a better retention ability. This latter claim was additionally substantiated with forty-four novice chess players (Marmèche & Didierjean, 2001), suggesting that knowledge generalization leads to the construction of abstract solving schemas, which promote in turn a better retention of contextdependent elements. A comprehensive study with forty-seven children examined in addition whether chess skill related to the judgement of the more abstract aspects of a chess position (Horgan & Morgan, 1990). The findings point to the fact that a growing level of chess skill is associated with a more abstract representation of the features of the chess position. A more recent study also corroborates that, apart from encoding the basic elements of a given chess position, highly rated players tend to encode more abstract and semantic chess relationships (Gong, Ericsson, & Moxley, 2015). Taken together, these findings support memory as a by-product of cognitive-perceptual processes, which might rely on a rich network of verbal and evaluative information while increasing in importance towards more positional or complex chess positions (Pfau & Murphy, 1988). Nevertheless, verbal rehearsal may have little influence on the memory for chess positions or the analytical processes involved in the selection of chess moves. This point of view highlights that a more suitable cognitive function to use in the explanation of individual differences in chess skill is likely to be embedded within long-term memory (Robbins et al., 1996). Similarly, an extension of the study by Holding and Reynolds (1982) reached the opposite conclusion regarding the role of pattern recognition (Schultetus & Charness, 1999). There was an obvious link between the quality of move selection and the subsequent recall performance, which necessarily implies a representation either in long-term memory or in a template structure. Furthermore, chess experts of a similar skill level albeit specialized in different chess openings were asked to solve problems within four kinds of chess positions arising from four different openings: Sicilian, French, Neutral, and Random (Bilalić, McLeod,

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et al., 2009). There was better performance in both remembering and solving problems concerning the respective area of specialization, indicating that knowledge of specific areas was more important than general problemsolving skills. This finding was argued to support the template theory hypothesis regarding the connection between templates with potential solutions and plans of action. Moreover, both the chunking and template theories contemplate the importance of abstract knowledge, whereby templates are deemed as conceptual prototypes that provide labels for characterizing extensive families of chess positions (Gobet, 1998; Gobet & Simon, 1996c). When dealing with chess problem solving, however, it is important to bear in mind the role of judgement and decision-making, two crucial cognitive processes that are embedded in the broader behavioural dimension of thinking.

3.3 Thinking Chess thinking has attracted considerable attention from expert chess players and scholars. For example, Nikolai Krogius suggests that there are two main ways of thinking when playing chess: concrete calculation and general assessment. Either thinking method might predominate depending on the specific moment and circumstances arising during a chess game (Krogius, 1976). A more recent chess training book suggests that chess playing comprises three main thinking strategies (Samarian, 2008): positional intuition; the ability to ‘see’ combinations; and the ability to calculate variations quickly and efficiently. Intuition differentiates master from average-level players because intuition predominates over logical thinking in chess (Kelly, 1985). In another view, emotional experience triggers the activation of thinking activity (Tikhomirov & Vinogradov, 1970). Moreover, other explanations of chess thinking refer to the term ‘apperception’, the application of unconscious principles for representing mental content and decision-making (Saariluoma, 1995, 2001). Nevertheless, the first in-depth work about chess thinking was that carried out by de Groot between 1938 and 1943 with renowned chess players such as Alexander Alekhine, Max Euwe, Paul Keres, Reuben Fine, Salo Flohr, and Savielly Tartakower (de Groot, 1965). Apart from laying down the foundations for the psychology of chess on cognitive and experimental grounds, the work by de Groot acknowledges the role of individual differences. The central aim of this work was to characterize the thought dynamics in chess regarding its organization, methods, and operations, in line with Otto Selz’s notion of thinking. More specifically, de Groot asked about the thought processes underlying chess skill, and about the singular ability of chess masters to spot the best moves usually overlooked by average chess players. These questions were examined through the verbalization of thought processes elicited when proposing the stronger chess move leading to the

thinking

31

solution of real chess positions. There were twenty-two chess players in this study: the aforementioned six grandmasters, four masters, two female champions of the Netherlands, five strong experts, and five skilled players. All players adopted similar thinking and decision-making strategies regardless of their chess strength. Stronger players were able to recognize at a glance the essence and correct move of the proposed chess position, however. The thinking-aloud methodology furnished some understanding about chess thinking methods and chess styles, albeit encompassing a considerable degree of inter-individual variability and ‘individual peculiarities and idiosyncrasies’ (de Groot, 1965: 313). Human judgement and decision-making in a variety of intellectual domains have been approached as pivoting on two thinking processes. Both processes have been referred to in many different ways. For example, the seminal work by Keith Stanovich and Richard West labels the processes as system 1 and system 2 (Kahneman, 2011; Stanovich & West, 2000). System 1 is a quick, automated process, operating effortlessly; system 2 is a slow, demanding process, usually involving complex computations and mental concentration. When judging a situation implying decision-making, both systems operate, at times in a close partnership. Whereas system 1 generates patterns of general ideas, system 2 builds specific methodical thoughts. System 1 and system 2 have also been termed ‘intuitive’ and ‘analytical’ components, operating together in human judgement and decision-making (Betsch & Glöckner, 2010). This systematic approach to thinking should also operate in the intellectually demanding endeavour of chess playing. Some thinking skills of expert chess players are certainly astonishing. Skilled child players are better able than non-chess-playing adults to predict their own performance even in a domain outside their own field of expertise (Horgan, 1992). Stronger chess players are also more accurate than weaker players at estimating a player’s strength from observing a particular self-created chess position (Reynolds, 1992). In addition, the estimation error of this prediction decreases when they see the subsequent moves generated in the position. The most striking advantage that expert players have over novices bears upon finding the best move in a given chess position, however (de Groot, 1965). This superiority is most likely to lie well beyond a simple advantage in perceptual or memory abilities, such as several high-level cognitive processing abilities that account more precisely for individual differences in chess skill. Some of these processes are forward-visual evaluation (Holding & Pfau, 1985), information processing (Horgan, Millis, & Neimeyer, 1989), pattern recognition (Schultetus & Charness, 1999), planning performance (Unterrainer et al., 2006), language (Nippold, 2009; Pfau & Murphy, 1988; Vasyukova, 2012), geometric and numerical skills (Ferreira & Palhares, 2008), and visuospatial and verbal encoding (Bachmann & Oit, 1992; Wagner & Scurrah, 1971). For example, chess players at higher levels of chess skill might be more skilful in

32

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foreseeing future positions by discerning non-redundant similarities, alternative goals, and more candidate moves in a given chess position (Holding & Pfau, 1985; Horgan et al., 1989). Why are there such remarkable individual differences in thinking efficiently about chess information? The scientific literature has put forward two main views anchored in the aforementioned system 1 (intuition) and system 2 (analytical) processes, which at the same time has been the object of a vigorous debate. The processes have been termed ‘pattern recognition’ and ‘search’, respectively. In one view, pattern recognition wields a dominant role and search a secondary role in chess thinking (Gobet & Simon, 1996b). This claim is largely based on the outcomes from simultaneous chess games between 1985 and 1992 played by the chess world champion at that time, Garry Kasparov, against national teams consisting of four to eight players. Under these conditions, Kasparov endured serious time constraints that prevented him from being involved in slow search. On the other hand, he was allowed to analyse, with the aid of a computer, 100 games from each of his opponents prior to each tournament. Because Kasparov played at a very high level under these circumstances, this was interpreted as supportive evidence for the prevalence of pattern recognition compared with search. Conversely, and in the view of the search approach, pattern recognition has been judged as inadequate to account for individual differences in chess skill, casting serious scepticism over the guiding premises of the pattern recognition theory (Holding, 1992; Holding & Pfau, 1985). From the search viewpoint, individual differences in chess thinking and chess skill are likely to depend on slow search processes, as portrayed by the SEEK (search, evaluation, and knowledge) theory. A crucial postulate of this theory is that the selection of chess moves proceeds by anticipating consequences with chess trees that are smaller and more discriminating, however, than chess trees built by machines. Moreover, the SEEK theory claims that there are notable individual differences in chess skill regarding search, evaluation, and knowledge, which remain with time constraints in fast chess and are not accounted for well solely by the pattern recognition approach. Thinking in chess is largely influenced by the available thinking time. Time is also a central key distinction between the system 1 and system 2 thinking processes. Therefore, comparing chess performance in fast and slow chess playing is an appealing approach to study chess thinking. There are two main chess-playing modalities regarding thinking time: fast (blitz) and slow games. Typically, chess players endure severe time constraints in fast blitz games, whereas they have a higher amount of available thinking time in slow games. Time constraints, therefore, might foster fast pattern recognition processes, albeit increasing in turn the

thinking

33

probability of committing devastating errors (Sigman et al., 2010). Moreover, time constraints might influence strategic behaviour and thinking during chess playing. A recent experiment with a large dataset of internet blitz chess games found that players changed their playing strategy when confronted with stronger opponents (Fernandez-Slezak & Sigman, 2012). Chess players adopted a prevention mode when playing stronger opponents, which involved investing a higher amount of thinking time together with greater move accuracy. This strategy did not imply increasing the probability of winning, however, because this extra time did not lead to significant improvements in the position. Increasing the probability of winning against stronger opponents would require a playing style more in accordance with that adopted when playing against an opponent with equivalent chess strength. Several stimulating studies have addressed the dual view of chess thinking by studying time constraints during chess playing, which have provided either supportive or unsupportive evidence for both pattern recognition and search as the predominant thinking processes in chess. An early study with six US players compared the quality of chess moves during standard games lasting forty moves in ninety minutes with blitz games lasting only five minutes for each player (Calderwood, Klein, & Crandall, 1988). Blitz time constraints hampered the quality of chess moves to a greater extent for weaker than for stronger players, which was considered as supportive of the pattern recognition approach. Furthermore, four chess players of different levels of expertise – grandmaster, international master, candidate master, and class B player – were asked to solve complex chess positions that required search thinking, and also to solve rapid decision-making, memory, and practice tasks (Campitelli & Gobet, 2004). The findings supported that search performance increases linearly with chess skill, in accordance with the SEEK theory. These findings also supported the pattern recognition theory in the memory and fast decision tasks, however. This study highlights that search might be undertaken occasionally in chess, whereas selective search and pattern recognition are also important for both fast and slow decisionmaking. There is indeed evidence that bolsters the pattern recognition view. For example, thirty-four US chess players were challenged to predict the moves of a chess game played by experts (Klein & Peio, 1989). Stronger players were more accurate than weaker players at predicting the moves of the game while also being more likely to advance the correct option as the first one to be considered. This set of findings was believed to reflect an underlying pattern recognition model as the main explanatory process of individual differences in chess skill. The effect of finding the best choice as the first one considered was replicated in another study that

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presented sixteen chess players with one middlegame position and three endgame positions (Klein et al., 1995). That experts are likely to rely on the generation of feasible options as the first ones considered was consistently corroborated. Moreover, similar verbal protocols to those used by de Groot were applied in the analyses of two chess positions with a sample of twenty-two intermediate and master chess players recruited from chess tournaments in Australia (Connors, Burns, & Campitelli, 2011). Masters had faster search abilities than intermediate players, through being better at generating more board positions resulting from the consideration of potential candidate moves. Masters did not search more deeply than intermediate players did, however. Thus, this study underlines the importance of fast pattern recognition for chess skill despite the fact that chess masters displayed faster and deeper searching abilities than intermediate players. Apart from studying chess players making decisions about chess positions, support for the pattern recognition approach has emerged from other kinds of data. For instance, a positron emission tomography (PET) study with blindfold chess compared the activation of brain areas in three kinds of tasks: attention, memory, and problem solving. These findings suggest that visuospatial representations of chess piece configurations are in fact prelearned chunks stored in long-term memory while implying highly automatic processing, which appears to support to a great extent the pattern recognition approach (Saariluoma et al., 2004). Another study with archival databases involving thirteen blitz chess tournament outcomes from the Netherlands, the United States, and Australia also confirmed the pattern recognition view (Burns, 2004). Fast processes such as recognition accounted for most of the variance in overall chess skill, whereas chess skill differences equalized when blitz games were being played, albeit to a lesser extent at higher levels of chess skill. In addition, although searching might be important for chess performance, it might also remain constant beyond a certain level of high skill. Moreover, there is alternative evidence about the pattern recognition approach, emphasizing instead the importance of search processes in explaining individual differences in chess skill. For example, the findings from the simultaneous chess games played by Kasparov, which support the pattern recognition predominance in chess (Gobet & Simon, 1996b), have been challenged by those advocating instead for the search view. The main argument hinges on the fact that the outcomes of games played between humans and machines indicate a stronger advantage for machines when the available thinking time is decreased. Such a trend emphasizes that human ability in search decreases with more stringent time constraints. Conversely, increasing the available thinking time favours search to a greater extent while enhancing chess-playing strength

thinking

35

(Lassiter, 2000). Moreover, the number and magnitude of chess blunders committed by twenty-three chess grandmasters were analysed by contrasting three kinds of chess games: slow, rapid, and rapid blindfold (Chabris & Hearst, 2003). A higher number of errors and larger blunders arose more often in rapid chess than in slow chess, whereas blunders were very similar in both respects in rapid and rapid blindfold chess alike. These findings were taken as opposed to the fast pattern recognition view, because grandmasters made a higher number of errors and irrecoverable mistakes with thinking time constraints. Similarly, a study comparing the games in slow and fast games of grandmasters, international masters, FIDE masters, and untitled players, with seventy-five players in each group, yielded analogous findings (van Harreveld et al., 2007). Time constraints resulted in a lessened predictive ability of individual differences in chess skill in blitz games than in slower games, suggesting that slow search thinking processes are important for both the stronger and the weaker players. A more recent study involving blitz games examined the time invested in chess moves apart from chess blunders while contrasting individual differences in chess skill (Chang & Lane, 2016). The two main findings contradict the fast pattern recognition approach. First, stronger players were more prone than weaker players to spend a considerable amount of time on a few moves. Second, the stronger players committed fewer blunders than weaker players. These findings support the notion that deep calculation is indeed still possible in fast chess, and that individual differences in the ability to search contribute meaningfully to individual differences in chess skill. The pattern recognition approach together with the concept of chunks has also been analysed in depth on theoretical grounds (Linhares & Freitas, 2010). With applied examples, this conceptual study reflects on the seminal work about perception in chess (Chase & Simon, 1973), by proposing the alternative ideas of experience recognition and analogies as the crucial elements of thinking in chess. In the view of Alexandre Linhares and Anna Freitas, chunks that form the simplest building blocks for more complex patterns should necessarily convey semantic information. Their argument appears to be in direct opposition to the pattern recognition approach. It questions the link between knowledge of very specific patterns (stored in long-term memory) and the actual selection of moves, and aligns better with findings that emphasize the importance of search processes during chess playing (Chabris & Hearst, 2003; McGregor & Howes, 2002). Perhaps a more reasonable perspective is one that highlights fast pattern recognition and slow search as both being equally important for chess skill. Harmonizing the two main viewpoints about the underlying thinking process of chess skill would imply that, with more

36

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thinking time, there might be greater chances of recognizing more patterns and applying search thinking to them (Chabris & Hearst, 2003). A very similar conclusion was also reached in another classical chess experiment with seventy-one chess players, who had to find the best moves to fifteen chess positions while thinking aloud (Moxley et al., 2012). Experts and less skilled players alike benefited from extra deliberation independently of the difficulty of the respective chess problem. Thus, both intuition (pattern recognition) and deliberative thinking (search) were deemed as mutually beneficial for chess skill. In another view, pattern recognition (i.e., chunking theory) in fact embraces search processes as well. Fernand Gobet, the leading researcher in the field of chess psychology, admits that it is a recurrent misunderstanding of chunking theory to presume it to be the unique or principal underlying factor to explaining individual differences in chess skill. A more integrated view holds that both the recognition of chunks and the exploration of candidate moves and their consequences underlie individual differences in chess playing skill (Gobet, 1997). Gobet argues that several of the premises raised by the SEEK theory (Holding, 1992) fail to provide evidence against the chunking theory. More specifically, the chunking theory is argued to provide the mechanisms of pattern recognition as an explanation of the search and evaluation of chess positions. Chess skill would therefore depend on large amounts of regular patterns of chess piece configurations stored in memory, together with selective search strategies within the chess tree. Knowledge structures gained through the acquisition of expertise in long-term memory would also increase short-term memory capacity when confronted with specific chess situations (Gobet, 1997; Gobet & Simon, 1998b). Chess thinking entails an intensive and complex combination of perceptual, memory, and thinking processes. In addition, chess thinking is influenced by a variety of psychological factors underlying individual differences. Moreover, chess playing even at an amateur level implies learning a considerable amount of domain knowledge, eventually extending over a lifetime to achieve a master level. Individual differences in brain functioning, intelligence, and personality are strongly associated with several learning processes in life domains such as education, work, and health. It is conceivable that they should play a role as well in learning and playing chess. Compared with other domains, however, the available scientific evidence linking individual differences in brain, intelligence, and personality with chess playing and chess skill is scanty, albeit encouraging. Individual differences highlight the variability in behaviour occurring between and within individuals, and between groups of individuals sharing a particular characteristic, such as when comparing novice with expert

thinking

37

chess players (Ackerman, 2014; Andrés-Pueyo, 1997; Colom, 2005). The next chapter delves into the individual differences approach to the psychology of chess, by analysing three main issues: the characterization and appraisal of individual differences; how individual differences can be addressed with a comprehensive model of adult intellectual development; and the controversy over heredity versus environment.

4 Individual Differences

Chess has served as a kind of Drosophila model for cognitive psychology. The previous chapter outlined three central cognitive processes involved in chess playing: perception, memory, and thinking. Information-processing models (Simon & Barenfeld, 1969; Simon & Chase, 1973; Simon & Gilmartin, 1973), the template theory of expert memory (Gobet, 1998; Gobet & Simon, 1996c), and system 1 and system 2 thinking processes (Kahneman, 2011; Stanovich & West, 2000) have provided a wealth of theoretical foundations and empirical findings useful for understanding how humans behave in an intellectually demanding environment such as chess. This body of knowledge emphasizes that there is a considerable degree of variation in perceptual, memory, and thinking processes, however, eventually leading to meaningful individual differences in chess skill. As highlighted in Chapter 3, the studies about the perception, memory, and thinking of chess players point out that stronger players perform better than weaker players at several attributes useful for chess. These attributes consist of encoding chess positions into larger perceptual chunks (Chase & Simon, 1973; Gobet & Simon, 1996a, 1996c; Horgan, 1992; Lane & Robertson, 1979), memorizing chess positions, and discovering semantic networks among pieces and chunks (Frey & Adesman, 1976), recognition accuracy (Goldin, 1979), and evaluative judgement abilities (Holding & Pfau, 1985; Horgan et al., 1989; Klein & Peio, 1989). Chess has also been suggested as an ideal model environment for the study of individual differences in the acquisition and development of expertise (Chabris, 2017; Charness, 1992; Gobet, 2016; van der Maas & Wagenmakers, 2005). In this view, studying individual differences in chess can contribute to unearthing how, when, and why humans differ when involved in a complex intellectual endeavour. Differential psychology is a useful conceptual and methodological approach to address such a different class of questions from those addressed so far from a cognitive psychology approach (Revelle, Wilt, & Condon, 2011). A considerable body of research within several fields and subfields of neurosciences and behavioural sciences advocates for the crucial significance of individual differences in explaining human behaviour. Several studies point out that there are consistent associations between brain anatomy 38

characterization and appraisal of individual differences 39 and functioning and inter-individual differences in motor behaviour and learning, perception, higher-level cognition, and intelligence and personality (Kanai & Rees, 2011). Furthermore, individual differences in core psychological constructs such as intelligence, personality, and vocational interests account for meaningful variations in a vast array of behaviours that are readily observable and of cardinal importance for contemporary society (Lubinski, 2000). This chapter is divided into three main sections. The first, on the characterization and appraisal of individual differences, describes the object of study and kinds of questions addressed by differential psychology, the definition and classification of psychological traits, and the main research designs in the field. The second section, on the individual differences in chess, introduces the intelligence as process, personality, interests, and intelligence as knowledge theory (PPIK) as an appropriate framework for integrating theoretical assumptions and contrasting hypotheses regarding the interrelationships of individual differences in psychological traits and chess skill. Moreover, it describes the Amsterdam Chess Test (ACT), a comprehensive psychometric device useful to evaluate individual differences in chess skill. Finally, the third section, on heredity versus environment, describes the most contentious issue within differential psychology – and probably within the social sciences. This section summarizes the main tenets of behavioural genetics, and some of the most remarkable findings in the two broad areas of intelligence and personality. Moreover, it highlights the relevance of the topic for chess research, particularly when addressing the talent versus practice controversy in accounting for the development of chess skill.

4.1 Characterization and Appraisal of Individual Differences Individual differences were probably first studied thoroughly back in the sixteenth century with the groundwork laid by the Spanish philosopher Juan Huarte de San Juan (Huarte de San Juan, 1593). Huarte de San Juan was one of the first authors to build a psychological framework based in biology. Two of his main postulates centred on the adaptation of education to the kind of skill possessed by each individual (Velarde-Lombraña, 1993) and on the role of individual differences in intelligence (Gondra, 1994). Nearly 300 years later, one of the most influential works for the development of differential psychology was that carried out by Francis Galton in the nineteenth century (Galton, 1869). Galton applied Charles Darwin’s evolutionary principles to human behaviour in an attempt to explain the foundations of intellectual abilities through the measurement of very basic sensory processes. Contemporary differential psychology enquires into the variability and regularities in behaviour across individuals and groups. It also focuses on differences in psychological attributes and dimensions, and on individual

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individual differences

variability regarding changes in behaviour across different moments and situations (Anastasi, 1937). From a comprehensive theoretical framework such as evolutionary psychology, individual differences are important for three main reasons. First, individual differences are very well documented. Second, individual differences have an important heritable component while exhibiting considerable stability over time. Third, stable individual differences have important consequences for evolution and adaptation to the circumstances encountered in real life (Buss, 2005, 2009). Individual differences can be classified into inter-individual, inter-group, and intra-individual differences (Ackerman, 2014; Andrés-Pueyo, 1997; Colom, 2005). Inter-individual differences characterize differences between individuals (e.g., differences in verbal aptitude in a group of youngsters). Inter-group differences characterize differences between different groups (e.g., differences in academic achievement between males and females). Intra-individual differences characterize differences within individuals elicited during maturation or ageing, or when going through some kind of external intervention (e.g., the change in foreign-language proficiency throughout secondary education). Intraindividual differences also characterize differences between distinct attributes within individuals that can be evaluated with standard psychometric instruments (e.g., differences in performance between verbal and numerical abilities). Another kind of individual differences can be termed inter-individual differences in intra-individual change, which characterize the differential performance of individuals when exposed to some kind of intervention or when enduring some kind of change throughout their lives (Ackerman, 2014). In general, individual behaviour manifests itself in a consistent and stable manner. Individuals are consistent and stable because they tend to display behavioural regularities across different situations and moments in time. Both consistency and stability are intimately related, with four main kinds of trait consistency being typically identified in the literature. Intra-individual differences in consistency (i.e., within trait dimensions), and ipsative consistency (i.e., between trait dimensions), centre on individual changes over time. Meanlevel consistency centres on whether groups change in trait dimensions over time. Rank-order consistency centres on the relative distribution of individuals within groups. For example, it has been suggested that the rank-order consistency of personality traits increases progressively towards the age of sixty (Caspi, Roberts, & Shiner, 2005; Roberts & DelVecchio, 2000). Moreover, an earlier study suggested that the intra-individual consistency of traits might be hierarchically organized, being higher for intelligence, moderate for personality, and lower for narrower traits such as self-esteem and life satisfaction (Conley, 1984). With regard to intelligence, a longitudinal analysis of psychometric intelligence carried out at ages eleven and seventy-seven supported robust intra-individual consistency in intelligence (Deary et al., 2000). With regard to personality, a common phenomenon such as mate selection (i.e.,

characterization and appraisal of individual differences 41 assortative marriage) is also related to intra-individual consistency in middle adulthood (Caspi & Herbener, 1990). Furthermore, mean-level consistency is associated with the similarity between two situations and the personality of the individual (Sherman, Nave, & Funder, 2010). Psychological traits are the narrower building blocks that constitute the basic architecture of differential psychology. Psychological traits describe the psychological attributes of interest concerning inter-individual variability in behaviour. There are at least ten useful qualities that are applicable to the identification of psychological traits (Eysenck & Eysenck, 1985; Zuckerman, 1991). 1. Psychological traits are useful dispositions for describing people and predicting human behaviour. 2. Psychological traits are concepts or constructs with a scientific foundation useful for describing individual differences. 3. Psychological traits are useful to place individuals within a continuous psychological dimension. 4. The responses to psychological testing characterize people’s traits, and they can also help to elucidate a given psychological theory. 5. Innate and environmental factors both determine psychological traits, though all traits have a moderate level of heritability. 6. Psychological traits have meaningful biological correlates, and consistent associations with physiological subsystems embedded in the nervous system. 7. The interaction between psychological traits and specific situations produces mental states. 8. Psychological traits show consistent intra-individual stability. 9. Psychological traits are universal and identifiable with factor analysis by sampling behaviour across different methods, sexes, ages, and cultures. 10. Psychological traits derived from humans parallel behavioural traits in non-human species. There are literally thousands of psychological traits amenable to a formal description with human language. Over 17,000 words in the English language were selected to describe human personality in one of the earliest studies about this topic (Allport & Odbert, 1936). For instance, multidimensional scaling statistical techniques applied to English-language terms yielded a structure as shown in Figure 4.1. The traits that are more beneficial for intellectual activities run from the most desirable at the top right corner, to the less desirable at the bottom left corner (Rosenberg et al., 1968). Figure 4.2 shows a potential classification of psychological traits into the two main broad domains of intelligence and personality (Andrés-Pueyo, 1997). Performance, ability, and skill are broad dimensions classified into the intelligence domain. Constitution, character, temperament, and personality

42

individual differences ACTIVE SYSTEMATIC

COLD UNSOCIABLE

PITILESS

PESSIMISTIC

CUNNING

IRRITABLE

INTELLIGENT

SKILFUL

CRITICAL

IMAGINATIVE

DOMINANT

TEMPERAMENTAL BAD ARROGANT SQUEAMISH

REFLEXIVE

CAUTIOUS RESERVED

RELIABLE

BORE MISCHIEVOUS FRIVOLOUS

HONEST TOLERANT

SUPERFICIAL HUMBLE

IMPULSIVE

GOOD

HELPFUL

IRRESPONSIBLE DULL

FUNNY

SUBMISSIVE

SINCERE SPONTANEOUS POPULAR

THICK PASSIVE

FRIENDLY

SOCIABLE

Figure 4.1 A structure of personality impressions from a multidimensional scaling approach (Rosenberg, Nelson, & Vivekananthan, 1968)

Performance

Intelligence

Ability

Skill Psychological traits

Constitution Character Personality

Temperament Personality

Figure 4.2 A simple classification of psychological traits into two broad dimensions: intelligence and personality

are broad dimensions classified into the personality domain. Performance is a quantitative outcome accorded a criterion, which meets the responses given by an individual to a cognitive task (e.g., academic achievement, a college admission test such as the SAT). Ability is the level of potential performance reached in an assortment of specific behaviours (e.g., the intelligence

characterization and appraisal of individual differences 43 quotient, the Elo chess rating). A skill is a set of competences exhibited when completing a task. In essence, a skill is the development of ability through practice or training (e.g., numerical, sport). Constitution is the biological structure of an individual in static terms, such as anatomical tissue, and dynamic terms, such as hormonal and biochemical functioning (e.g., height, second to fourth digit ratio). Temperament encapsulates the collection of emotional characteristics of behaviour somehow expressing the genetic determinants of personality (e.g., neuroticism, impulsivity). Character is the combination of traits related to attitudes, values, and feelings guided by culture (e.g., attitudes, beliefs). Finally, personality is the combination of factors related to constitution, temperament, character, and (for some authors) intelligence. The measurement and evaluation of individual differences can be undertaken at three distinct levels of analyses underpinning distinct theories and measurement systems (Colom, 2005), as shown in Figure 4.3: the trait level, the (a)

Level

Theory

Trait FACTORS

FACTORIAL

Psychometric testing

Cognitive PROCESSES

COGNITIVE

Experimentation

Biological ORGANISM

BIOLOGICAL

Psychophysiological / biological

(b)

Measurement

Target Behaviour Analyses of variability Cognitive abilities Inter-individual

Tasks

Perceptual process (P)

Spatial process (S)

Inter-group Intra-individual

Personality traits

Figure 4.3 There are different levels of analysis and measurement in differential psychology; the levels of analyses (traits, processes, and biological) can be combined to analyse the variability in a given target behaviour

44

individual differences

(a)

Year of Birth (cohort)

1970 1960 Inter-individual differences 1950 1940

1980 1990 2000 2010 Year of observations / measurement (b)

Year of Birth (cohort)

1970 Intra-individual differences 1960 1950 1940

1980 1990 2000 2010 Year of observations / measurement (c)

Year of Birth (cohort)

Inter-individual differences

Intra-individual differences

Inter-cohort differences

1970 1960

1980

1990

2000

2010

Year of observations / measurement

Figure 4.4 Cross-sectional, longitudinal, and sequential research designs to evaluate inter-individual variability

cognitive level, and the biological level. The foundations of each level of analysis involve factorial, cognitive, or biological theories and their corresponding hypotheses. The associated measurement systems correspond to psychological testing, experimentation, and psychophysiological or biological

individual differences in chess

45

measures. The variability in behaviour (i.e., inter-individual, inter-group, and intra-individual differences) can therefore be evaluated by combining different personality and intelligence traits at any level of analysis. From a developmental approach, individual differences can be examined with three differentiated research designs: cross-sectional, longitudinal, and sequential (Figure 4.4). In a cross-sectional design, individuals of different ages or the same age are observed at the same temporal point. This design is particularly useful for providing information about inter-individual differences. With a longitudinal design, it is possible to observe the same individuals during a certain period and provide information about intra-individual differences. Finally, a sequential design combines the characteristics of both crosssectional and longitudinal designs. In a sequential design, participants from different ages are selected and evaluated. This latter design allows the assessment of inter-individual differences as potential predictors of the intraindividual change, or whether intra-individual changes vary over time (Little, Schnabel, & Baumert, 1998).

4.2 Individual Differences in Chess Chess is a demanding intellectual activity with systematic and universal foundations. It involves an intensive application of broad psychological attributes, such as perception, memory, and thinking. In addition, it subsumes an extensive amount of theoretical and practical knowledge about openings, endgames, strategical and positional characteristics, tactical combinations, and specific analytical and thinking methods. Learning and mastering this large body of knowledge requires a relatively long time, and also entails a great motivational effort. The inter-individual variability in these factors and processes is noteworthy, which determines to a great extent individual differences in chess performance and chess skill. Together with chess thinking methods, the variability in chess performance and chess skill have been considered to pivot on the connections between emotional, motivational, and cognitive processes (Tikhomirov & Vinogradov, 1970). The intelligence as process, personality, interests, and intelligence as knowledge theory (PPIK) provides a comprehensive framework by which to integrate these individual differences, in accordance with both theoretical assumptions and empirical findings (Ackerman, 1996; Ackerman & Heggestad, 1997). Several empirical studies support the interplay of individual differences in ability, personality, and interests in the structure and development of intellectual performance (Hambrick, Meinz, & Oswald, 2007). The PPIK theory partly stemmed from three crucial inconsistencies concerning the assessment of adult intelligence:

46

individual differences

1. the manifest contrast in the meaning of intelligence assessment for children and adults with intelligence quotient (IQ) tests; 2. the discrepancies in the poor performance of the elderly in measures of cognitive abilities when compared with their daily functioning; and 3. the correlations below 0.60 between measures of cognitive abilities and educational and job performance. Aiming to override these limitations while providing a more straightforward theory of adult intellectual development, Phillip Ackerman has outlined a comprehensive and sound basis for evaluating the nature and interrelationships of individual differences during adult development. The PPIK theory is built on extant models of intelligence (Carroll, 1993; Cattell, 1987; Vernon, 1950), personality (Eysenck, 1952; McCrae & Costa, 1997), and vocational interests (Holland, 1959, 1996). Moreover, the PPIK framework provides a robust empirical background based on meta-analytic findings (Ackerman & Heggestad, 1997). The four main broad components of the PPIK theory are intelligence as process (fluid intelligence, Gf), personality, interests, and intelligence as knowledge (crystallized intelligence, Gc). Each of these broad components comprises narrower traits that can be evaluated when framed within a specific intellectual domain such as chess. Figure 4.5 shows a tentative PPIK representation adapted to the chess domain. The four broad components of the PPIK theory are depicted in bold face, and hierarchically linked to their respective narrower traits with one-headed arrows. The narrower traits associated with intelligence as process (Gf) and interests are as suggested by the PPIK theory but for the long-term memory factor, and for the visual abilities factor, which replaces the spatial rotation factor suggested by Ackerman. These factors could be encapsulated under the umbrella of information-processing factors, which tend to decline with ageing. Discontinuous double-headed arrows represent correlations between the factors across the four main PPIK components. Realistic and investigative interests are associated with intelligence as process (Gf), while investigative and artistic interests are associated with intelligence as knowledge (Gc). The personality and intelligence as knowledge (Gc) components incorporate substantial changes from those indicated by the PPIK theory in line with the available findings in the chess domain. The personality component includes motivation, will power, and emotional regulation, because individual differences in these traits relate to chess skill in some studies. Openness and typical intellectual engagement were already suggested in the initial formulation of the PPIK theory. The intelligence as knowledge (Gc) component includes some of the most relevant elements that conform to the knowledge base of chess players. For example, there are a huge range of chess writings dealing with the great variety of chess openings, their main lines, and their variants and subvariants.

individual differences in chess

47

This stage of the game is particularly important, because playing it well has a remarkable influence on the course of the game. An estimation of the opening knowledge of chess players across different levels of expertise suggests that chess players at the master level are able to memorize about 100,000 opening moves (Chassy & Gobet, 2011). Other core concepts contributing to the knowledge weaponry of chess players are positional and tactical principles, which are readily taught to beginners in chess-playing initiation courses. On the other hand, endgames correspond to the final stage of a chess game, when there are very few pieces remaining on the board. Endgames raise many specific schemes and subtleties, demanding thoughtful and intensive study in order to master them. Furthermore, Figure 4.5 indicates that the PPIK theory can be used to address both the structure and development of chess expertise (Ericsson et al., 2006; Gobet, 2016). In this view, the structure of chess expertise can be examined by looking at the pattern of traits most determinant of chess skill (e.g., inter-individual differences, inter-group differences), whereas the development of chess expertise can be examined by looking at the characteristics and properties of the change over time in those traits (e.g., intra-individual differences, inter-individual differences in the intra-individual change). Working Perceptual Visual Reasoning memory speed abilities

Motivation Emotional Openness Will power regulation TIE

Intelligence as process (Gf )

Intelligence as knowledge (Gc)

Openings Positional Tactical Endgames principles principles

Personality

Realistic Conventional

Interests

Enterprising Central Weak Pawn Open Combinations squares squares structures lines Piece exchanges

Investigative Artistic

Social

Structure of Chess expertise Time Development of Chess expertise

Figure 4.5 The PPIK theory applied to the chess domain (intelligence as process, personality, interests, intelligence as knowledge: Ackerman, 1996); Gf = fluid intelligence; Gc = crystallized intelligence; TIE = typical intellectual engagement

48

individual differences

Some of the links across the broad factors suggested by the PPIK framework have been advanced for instance in chess training books. For example, a recurrent question is whether these factors influence the choices that chess players make between valid continuations that are seemingly equivalent at first glance (Kotov, 1971; Samarian, 2008). Furthermore, earlier scientific works about the psychology of chess have also highlighted the importance of the factors embedded in the PPIK theory. Several general features of chess playing might influence individuals in a similar way in the emotional plane (Tikhomirov & Vinogradov, 1970). On the other hand, personal and temperamental differences on the part of chess players have been suggested as meaningfully shaping chess-playing style (Cleveland, 1907). Moreover, high-level intellectual processes such as combination power, finding logical regularities, and reaction time in relatively simple tasks, such as checking calculations, have been advanced as causal factors of chess talent (Djakow et al., 1927). In the work about thought processes in chess (de Groot, 1965), chess positions were presented to chess players with varying skill levels (e.g., grandmasters, masters, experts, and unskilled players). De Groot suggests that subtle systematic individual differences concerning problem-solving strategies arose, particularly when players were confronted with difficult chess positions. More specifically, de Groot suggests several areas, broad traits, and psychometric tests whereby individual differences should arise regarding the structure and development of chess talent, which can readily be identified within the PPIK framework: 1. 2. 3. 4. 5. 6. 7. 8.

higher scores in tests of spatial abilities; higher scores in tests of verbal abilities; an extensive knowledge base; an outstanding learning ability from past experience; the ability to test novel hypotheses; deep motivation for trying and analysing; an innate disposition to integrate thinking, playing, and fighting; and unknown personality factors;

Because chess implies an intensive application of high-level cognitive processes (de Groot, 1965; Djakow et al., 1927), chess research has typically placed the greatest emphasis on the PPIK components of intelligence as process (Gf) and intelligence as knowledge (Gc). Intellectual abilities have been repeatedly put forward when seeking potential explanatory causal factors for individual differences in chess skill. For example, pioneering work from informationprocessing models, perception, and memory judged the appropriateness of abilities involving abstract relations for chess, far beyond the organization of chess information into chunks. Furthermore, although there appeared to be a lack of evidence regarding the superiority of stronger players on basic intellectual factors, exceptional abilities were argued as indispensable at

individual differences in chess

49

a World Chess Championship level (Chase & Simon, 1973; Simon & Chase, 1973). The interest in intellectual factors as studied in the chess domain is further exemplified by more recent meta-analytic reviews, which have summarized the available empirical evidence to date (Burgoyne et al., 2016; Sala, Burgoyne et al., 2017). On the other hand, studies involving the personality of chess players together with the interests implied in becoming involved in a long and demanding chess learning process are much more scarce (Grabner, Stern, & Neubauer, 2007).

(a)

(b)

(c)

Figure 4.6 Sample items from the Amsterdam Chess Test in the choose-a-move, predict-a-move, and recall subtasks (van der Maas & Wagenmakers, 2005)

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individual differences

The PPIK theory is a useful conceptual approach for studying the association of several traits with individual differences in chess skill. The PPIK framework encompasses four broad components that are helpful to organize and examine the structure and development of the psychological traits presumed to have a bearing on chess skill (Ackerman, 2007). Is there any psychometric test to evaluate individual differences in traits embedded within the PPIK components, however? Yes, there is. The Amsterdam Chess Test (ACT) is an empirical tool that allows for the evaluation of traits from some of the four broad components of the PPIK theory (van der Maas & Wagenmakers, 2005). The development of the ACT is probably the most comprehensive psychometric study undertaken about individual differences in chess. Using data from a considerable sample of chess players during a chess tournament in the Netherlands (N = 259), this study describes the development of the ACT, a comprehensive computerized instrument aimed at calibrating chess skill. The development of the ACT was motivated by four main issues: the lack of a psychometrically sound measurement device to evaluate chess skill; the in-depth evaluation of psychometric techniques within an intellectually demanding yet systematic domain; the examination of the nature of chess proficiency; and for pragmatic reasons related to the initial evaluation of chess skill. The ACT comprises five subtasks delivered through a computer: a choosea-move subtask (two tests, A and B), a chess motivation questionnaire, a predict-a-move task, a verbal chess knowledge questionnaire, and a recall subtask (Figure 4.6). Each of the two tests from the choose-a-move subtask comprise forty typical chess problems, including twenty tactical items, ten positional items, and ten endgame items, all of them to be completed within thirty seconds. The sample tactical item shows that the correct answer is the move e1-h1+, which scores one point, whereas any other answer scores zero points. The motivation questionnaire comprises thirty items measuring three motivational traits: positive fear of failure, negative fear of failure, and desire to win. There are ten seconds to complete each of these items, which are answered on a five-point ‘disagree’–‘agree’ scale. The predict-a-move subtask comprises forty-two items corresponding to the course of a real chess game (Liss versus Hector, Copenhagen, 1996), with thirty seconds allotted to each item. The participant is asked to suggest the best continuation for the white pieces, with a scale from zero to five points. For the sample item, the suggested moves scored either three (a2-a4), two (c3-e4), or one (a2-a3 or f3-e5) points, while any other move scored zero points. The verbal chess knowledge questionnaire comprises eighteen four-choice items about the opening, positional, endgame, and visual imagery aspects of the game. There are fifteen seconds to complete each of these items. The recall subtask consists of eighteen items. An initial chess diagram is presented for ten seconds (left diagram in Figure 4.6 c), then

heredity versus environment

51

a blank screen follows for two seconds, and then an empty chessboard with one square marked by a circle (square d6 in the right diagram in Figure 4.6). The participant has to identify within ten seconds the piece in the initial diagram that was occupying the square marked with the circle in the empty diagram. The correct answer for the item sample is ‘empty square’. Higher scores in the five subtasks from the ACT indicate a higher level of the respective evaluated traits. In the study describing the development and application of the ACT (van der Maas & Wagenmakers, 2005), the subtasks of this instrument were highly predictive of the variability in chess skill as measured by the Elo rating (75%), together with sex, age, and the number of chess games played the season prior to the data collection. Unfortunately, even though the ACT provides a comprehensive evaluation of chess skill independently of the commonly used Elo rating, it has been rarely used in applied research about individual differences in chess. As suggested by the authors of the ACT, the test could be used to estimate individual differences in chess skill independently of the Elo chess rating.

4.3 Heredity versus Environment What are the reasons and motives leading individuals to play chess? More importantly, why do only a few individuals achieve a remarkable performance in the game? When somebody reaches a grandmaster chess level, is such an accomplishment a matter of innate predisposition, or does it depend on a long period devoted to intensive and specific chess training? These are recurrent issues that frequently loom large in differential psychology and chess research. Whether behaviour depends on the influence of genes (nature) or on the influence of the environment (nurture) is arguably the most cogent debate in social sciences. The problem has elicited a considerable deal of research effort to date, but the controversy might be already over. It has been claimed that the distinction between nature and culture as two differentiated entities affecting behaviour should be dismissed, because organisms inherit regularities from both genes and the environment (Buss, 2001; Pinker, 2002; Tooby & Cosmides, 1990, 2005; Tooby, Cosmides, & Barrett, 2003). The influence and mechanisms of both systems in determining behaviour is one of the most groundbreaking topics in the field (Bleidorn et al., 2010; Kanai & Rees, 2011; Plomin et al., 2014). How genes and environment combine to shape human behaviour was thought to articulate around six main lines of research (Anastasi, 1958): 1. the associations between physiological variables and behavioural variations; 2. the role of prenatal physiological factors in later development;

52 3. 4. 5. 6.

individual differences the influence of early experiences on later behaviour; the cultural differences in child-rearing concerning development; the mechanisms of somatic and psychological relationships; and the development of twins and their social environment.

More modern methods and technologies have served to implement these lines of research, such as genome-wide sequencing technologies (Mardis, 2009), knowledge management systems (Ashburner et al., 2000; Blanch, García, Planes, et al., 2017), and statistical and conceptual developments (Franic et al., 2013; Günther, Wawro, & Bammann, 2009; Hodgins-Davis & Townsend, 2009). Human behavioural genetics is the scientific field addressing how the genotype, the inherited component encoded in the genes, interacts with the environment to give rise to complex traits or phenotypes (Plomin & Rende, 1991). The main aim in human behavioural genetics is to discover how the variation in traits emerges from the complex interaction between inherited components and environmental influences. Three main laws in human behavioural genetics are that (1) all human traits are heritable, (2) the effect of being raised in the same family is smaller than the effect of genes, and (3) a substantial portion of the variation in complex human behavioural traits is unaccounted for by the effects of genes or families (Turkheimer, 2000). From this viewpoint, genes and environments embed into a development system, eventually producing individual differences in behaviour. With additive and independent genetic and environmental effects, a given trait (x) in a population would arise from the combination of genetic (G) and environmental (E) factors, as shown in Equation 3.1, where e is a quantity due to trait measurement unreliability. Within a given population, and as shown in Equation 3.2, the variability in the trait (variance ~ standard deviation) is due to the variability in genetic (var(G)) factors, the variability in environmental (var(E)) factors, and the correlation of genetic and environmental factors (2Cov(G,E) (Hunt, 2011). x ¼GþE þe

3:1

varðxÞ ¼ varðGÞ þ varðEÞ þ 2CovðG; EÞ

3:2

The extent to which the variability in the trait is heritable in the observed population depends on the proportion of phenotypic variance due to genotypic variance across individuals in the population (Plomin, DeFries, & Loehlin, 1977; Turkheimer, 1991, 1998). This is typically characterized with the heritability coefficient (h2), as shown in Equation 3.3, keeping in mind that h2 is applicable only to populations, not to individuals. h2 ¼ varðGÞ=varðxÞ

3:3

heredity versus environment

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Human behavioural genetics draws on data from three kinds of studies. Family studies compare members of the same family who share genetic and environmental components. Twin studies compare monozygotic (MZ) and dizygotic (DZ) twins who share 100 and 50% of genetic components, respectively. Adoption studies include individuals who share environmental factors only, together with individuals who share both genetic and environmental factors. In general, the extent to which individuals of varying genetic relatedness are more similar in a given trait supports a greater influence of either genetic or environmental factors. For instance, and in a twin study, a higher correlation between MZ than between DZ twins in a given trait would support a higher genetic predisposition regarding that trait (Plomin et al., 1997). The available empirical evidence from human behavioural genetics supports the view that most, if not all, individual differences in behaviour are partially heritable. Genes affect complex behaviour, but so do shared and non-shared environments. The shared environment comprises the influences that make family members similar to one another. The non-shared environment comprises the effects that make family members different from one another, such as the individual experiences of children with their peers, and the facets of parenting that are not shared in the same family (Plomin & Daniels, 1987; Turkheimer & Waldron, 2000). For example, both genetic and environmental factors might have an equivalent weight in determining group differences in intelligence (Rushton et al., 2007). Thus, the environment is also a fundamental aspect in shaping development and complex behaviour when interacting with genes, because it contributes to changing subsequent behaviour and the expression of genes in a reciprocal cycle (Plomin & Petrill, 1997; Plomin & Rende, 1991; Turkheimer, 1991, 1998, 2000). The combination of variation in genotypes and in environments in producing individual differences in development was addressed in the early 1980s, suggesting three kinds of genotype → environment effects: passive, evocative, and active (Scarr & McCartney, 1983). The passive kind takes place in genetically related families, with parents providing genes and environments for their offspring. The evocative kind contemplates those instances whereby different genotypes evoke different responses from the environment. The active kind consists in the choices made by individuals from different environments, which tend to match their motivational and intellectual genetic endowment. Two compelling additional propositions of this model are that, during development from infancy to adolescence, the effect of the passive kind decreases while the effect of the active kind increases. A later bioecological model advanced three testable hypotheses pivoting on the concept of proximal processes as the core organism–environment interaction mechanisms directly implicated in development. Proximal processes comprise parent–child and child–child activities, group or solitary play, reading, learning new skills,

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problem solving, performing complex tasks, and acquiring new knowledge. In this view, weaker proximal processes impair genetic potentials, whereas stronger proximal processes enhance genetic potentials. More specifically, stronger proximal processes would allow for the accomplishment of important developmental outcomes, such as coping under stress, acquiring knowledge, and establishing rewarding relationships (Bronfenbrenner & Ceci, 1994). 1. The heritability (h2) will be higher with stronger proximal processes, and lower with weaker proximal processes. 2. Strong proximal processes will contribute more to developmental competence in advantaged and stable environments. Strong proximal processes will buffer more developmental dysfunction in disadvantaged and disorganized environments. 3. Strong proximal processes will contribute more to developmental competence for those individuals in disadvantaged and disorganized environments when they are exposed extensively to circumstances rich in developmental resources. Genetic and environmental underpinnings of personality and intelligence have stimulated a great deal of research (Caspi et al., 2005; Plomin, Owen, & McGuffin, 1994). Meta-analytic findings suggest that 40% of the variation in personality is due to genetic influences (Vukasovic & Bratko, 2015). Moreover, genetic and non-shared environmental factors account for personality changes that tend to stabilize at later ages (Hopwood et al., 2011). For instance, findings with over 21,000 sibling pairs indicate more stable genetic and environmental effects on personality with ageing, and with additional increments of environmental effects on phenotypic stability into adulthood (Briley & Tucker-Drob, 2014). Findings supportive of the universality of human personality advocate in addition for a consistent biological basis of personality (Yamagata et al., 2006). The association of personality traits with genetic polymorphisms (5HTT LPR, DRD4 c4t, DRD4 length, DRD2 A1/A2, DRD3 A1/A2) have rendered non-significant findings after controlling for allele frequencies and unpublished data, however (Munafó et al., 2003). As with personality, there seems to be a weak association between general intelligence (g) and single-nucleotide polymorphisms in several genes (DTNBP1, CTSD, DRD2, ANKK1, CHRM2, SSADH, COMT, BDNF, CHRNA4, DISC1, APOE, and SNAP25). This finding has been attributed to low statistical power linked to limited sample sizes (Chabris et al., 2012). In contrast, general intelligence might have a consistent polygenic structure underlying multiple tiny effects from different gene loci and their combinations (Chabris et al., 2013). This polygenic approach to the genetic influence of complex traits had, in fact, already been advanced in earlier studies about the genetic basis of human behaviour (Bouchard & McGue, 1981; Plomin et al., 1994), and is actually being implemented at present with modern genome-wide

heredity versus environment

55

association scan applications (McCrae et al., 2010). Several twin and adoption studies point to a considerable amount of variability in intelligence being accounted for by genetic factors (Johnson et al., 2007; Plomin & Spinath, 2004; Posthuma, de Geus, & Boomsma, 2001). Moreover, studies with a focus on the development of intelligence highlight three main findings: genetic influences increase throughout the lifespan; the importance of shared environment in childhood and of non-shared environment beyond adolescence; and stronger genetic influences in more favourable social and economic conditions (Plomin & Petrill, 1997; Plomin & Spinath, 2004; Tucker-Drob & Briley, 2014; TuckerDrob, Briley, & Harden, 2013). Behavioural genetics has also focused on socially relevant outcomes produced in important contexts such as family, work, and education. In examining the affective climate in over 600 families, genetic factors accounted for 37%, whereas shared environmental factors accounted for 19% of the variability in the expression of negativity such as anger or hostility, as opposed to the expression of positivity such as warmth or affection (Rasbash et al., 2011). In the work realm there are several explanatory mechanisms involving genetic effects on work attitudes and leadership (Ilies, Arvey, & Bouchard, 2006), positive and negative affectivity associated with job satisfaction (Ilies & Judge, 2003), and coping with work demands (Maas & Spinath, 2012). Because personality and intelligence have been shown to be highly heritable, and intelligence is a very robust predictor of educational achievement (Aluja & Blanch, 2004; Blanch & Aluja, 2013; Deary et al., 2007; Poropat, 2009), educational accomplishment has attracted considerable attention from human behavioural genetics. For example, the CoSMoS German study with ninety-seven MZ twins and 183 DZ twins corroborated a meaningful heritability of cognitive ability, self-perceived abilities, and academic achievement (Gottschling et al., 2012). Moreover, data from a sample in the Minnesota Twin Family Study (MTFS) suggested that shared and non-shared environmental influences on educational achievement were stronger at low intelligence quotient (IQ) values, decreasing with IQ increments (Bouchard & McGue, 1981). In contrast, genetic influences on educational achievement were reported as weaker at lower IQ, while increasing at higher IQ (Johnson, Deary, & Iacono, 2009). Further data from the Twins Early Development study (TEDS) confirmed that intelligence accounted for the higher proportion in the heritability of academic achievement. Individual differences in other factors, however, such as self-efficacy, personality, and behavioural problems, accounted for nearly as much heritability of academic achievement as intelligence did, supporting additional influences of other traits with a robust genetic basis (Krapohla et al., 2014). Genome-wide association studies (GWASs) with over 126,000 individuals have identified genetic variants associated with educational achievement (Rietveld et al., 2013), while linking polygenic scores (PSs) with educational attainment scores and relevant outcomes in life

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individual differences

development such as adult economic outcomes, the acquisition of speech and reading skills, geographic mobility, mate choice, and financial planning (Belsky et al., 2016). As far as it is known, there are no behavioural genetics studies with chess players. Nonetheless, the controversy of nature versus nurture has also emerged to some extent in chess studies. For instance, a comparison of sixteen novice, eight intermediate, and eight expert chess players suggested a greater advantage for experts in perceptual encoding, which, it is argued, depends on chess experience and knowledge rather than on an innate predisposition involving a perceptual or memory superiority (Reingold et al., 2001). Similarly, another comparison of forty children with forty adults (twenty novice and twenty expert chess players in children and adults alike) supported the view that specific chess knowledge impinged clearly on memory performance. The advantage of children was argued to be associated with innate memory abilities important for chess, however, in contrast to adults, who would be more dependent on learning and accumulated knowledge from experience (Schneider et al., 1993). The nature versus nurture controversy is of considerable theoretical importance for the development of chess expertise, particularly when considering whether chess skill depends on individual dispositions or on the effects of practice. For example, some authors suggest practice as the crucial element for the development of chess expertise (Ericsson & Charness, 1994; Ericsson, Krampe, & Tesch-Römer, 1993). In contrast, other authors argue that practice is a necessary but not a sufficient condition for achieving an expert chess level, suggesting that only a modest part of the variability in chess skill is due to the effects of practice (Campitelli & Gobet, 2011; Hambrick et al., 2014). In any event, comprehensive theoretical accounts about the development of expertise, including chess, have attempted to integrate multiple genetic and environmental factors (Ericsson et al., 2006; Gobet, 2016; Simonton, 2014a, 2014b; Ullén, Hambrick, & Mosing, 2016). This topic is addressed in greater depth in a later chapter, on expertise in chess (Chapter 8). An initial place to look for individual differences in chess skill is the psychophysiology and brain functioning of chess players, however; a fascinating theme that is addressed in depth in the next chapter.

5 Psychophysiology and Brain Functioning

Chess is a natural domain appropriate to study issues related to individual differences in psychophysiology and brain functioning. It has simple and universal rules, it implies higher-order cognition and domain-specific knowledge, and the Elo rating is a valid and reliable quantitative measure of chess performance (Charness, 1992; Gobet, 1998; Gobet & Charness, 2006; Simon & Chase, 1973; van der Maas & Wagenmakers, 2005). Chess is analogous to other sports regarding biochemical, physiological, neuronal, and psychological aspects. Because of its main focus on intellectual performance, however, chess is unique compared to other sports of a more physical nature. The energy required by neuronal activation is delivered by oxygen and glucose through the vascular system. Higher neuronal activity implies higher demand for oxygen, which increases in turn the brain blood volume and flow (Golf, 2015a). An increasing amount of studies address psychophysiological and brain activity parameters during chess playing. For instance, there is a recent multimodal magnetic resonance imaging (MRI) dataset from twenty-nine professional chess players available to interested researchers, which includes phenotype data such as age, sex, education, and intelligence measures (Li et al., 2015). Moreover, comprehensive reviews highlight that brain anatomy has robust links with inter-individual differences in motor behaviour and learning, perception, cognition, intelligence, and personality (Kanai & Rees, 2011). Because chess is a highly demanding intellectual activity involving several of these attributes, the psychophysiology and brains of chess players constitute an attractive object for study in a controlled domain. This chapter comprises two main areas of enquiry. The first focuses on the psychophysiology of chess players by reviewing research works about the heart rate (HR), respiratory variables, hormones, and the issue of doping in chess. This area encompasses a smaller amount of studies comprising physiological functioning events other than brain functioning. The second area of enquiry focuses on the brain activity of chess players with techniques such as electroencephalography, functional magnetic resonance imaging, magnetic resonance imaging, magnetoencephalography (MEG), positron emission tomography, and singlephoton emission computerized tomography (SPECT). 57

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5.1 Psychophysiology and Chess Most studies addressing psychophysiological parameters in chess have been framed in terms of the human stress response model. This model proposes that activation of the sympathetic nervous system, a parasympathetic withdrawal, and heightened activity of the hypothalamic–pituitary–adrenal axis contribute to physiological and mental improvements to meet environmental demands (Sapolsky, 1996; Selye, 1975). The chess domain has been used to evaluate such psychophysiological stress mechanisms under a stressful condition involving a high cognitive workload. One of the most meaningful physiological markers in stress processes is the heart rate (HR), which measures the heart’s contractions or beats per minute (bpm), with a normal range of between 60 and 100 bpm in a resting state, and with abnormalities in this range being associated with a higher risk of cardiovascular disease (Fox et al., 2008). In chess, HR is frequently associated with several playing circumstances, such as committing an irrecoverable mistake that usually leads to a defeat (i.e., a blunder), the evaluation of a difficult move, a piece sacrifice, a hazardous defence, or a winning move (Golf, 2015a). A pioneering study examined parameters such as psychological maximum stress, autonomic excitability, circulatory conditions, and the long-term metabolic load during an eighteen-day tournament with fourteen chess players (Pfleger et al., 1980). Over 70% of the participants showed increased cholesterol levels in blood throughout the chess tournament, whereas their autonomic excitability and circulatory parameters were deemed to be fully comparable to those reported in other sports. Heart rate variability (HRV) has also received a certain degree of attention. This physiological parameter indicates the time between two heartbeats. A low HRV is associated with increased mortality, the incidence of cardiac events, and a heightened risk of sudden cardiac death (Achten & Jeukendrup, 2003). For example, cardiac events such as high-frequency heart rate variability (HF-HRV) relate to a psychometric measurement of helplessness/hopelessness, as the opposite trait to optimism/control, applying to nine active players above 2300 Elo rating points (Schwarz et al., 2003). Increased hopelessness associated with a reduced HF-HRV, suggesting a consistent negative correlation between negative mood states with autonomic nervous system disruptions, and with observable cardiac events. In addition, another intriguing finding is that, despite the very broad and basic nature of HR as a psychophysiological marker, it related to cognitive events during twenty-five chess games played by nine chess players within a range of about 2021 to 2216 Elo rating points. Furthermore, framing and processing the attainment of a specific goal through planned action and analysing variations and opponent’s blundering predicted meaningful increments in the incidence of HRV, with a 75% chance of a reliable detection of HRV changes for the analyses of chess variations (Leone et al., 2012). It has also

psychophysiology and chess

59

been suggested that HRV decreased during a rapid game between an elite human chess player with an Elo rating of 2550 points and a machine (Fuentes et al., 2018). These meaningful connections between HRV and cognitive processes run parallel to experimental outcomes in a sustained attention task, whereby there was higher HRV in a group with high physical fitness compared with one with low physical fitness from the general population (Luque-Casado et al., 2013). In addition to HRV, there is evidence on the association of the stress caused by chess playing with respiratory variables such as ventilatory flow (VF), tidal volume (Vt), breath frequency (bF), O2 consumption (VO2), CO2 production (VCO2), and respiratory exchange ratio (RER), among others (Troubat et al., 2009). Measures of these parameters were obtained from twenty chess players with between 1250 and 2170 Elo rating points when playing a single one-hour game against computer software set at 100 Elo points above each human’s player respective Elo rating. All measures were obtained before and during the game. There was a meaningful increment in HR throughout the game, supporting the sympathetic nervous system stimulation view. Furthermore, the HR was higher at the start of the game, then decreased in the latter stages, suggesting that energy expenditure switched from carbohydrate to lipid oxidation. This body of evidence is interesting in its own right for the field of human stress, as it provides sound findings from an ecologically valid and well-controlled domain such as chess. On the other hand, however, it is somewhat surprising that none of the aforementioned studies has addressed the impact of individual differences in chess skill as related to the obtained psychophysiological findings. Moreover, there is a remarkable dearth of studies addressing the role of certain hormones on chess performance. For example, testosterone has been associated with chess tournament outcomes. Winners of chess tournaments showed higher concentrations of testosterone than losers did, even before actually playing the games. Heightened testosterone appeared to reinforce a dominance pattern of behaviour and aided the winning of these particular chess contests (Mazur, Booth, & Dabbs, 1992). The sporting nature of chess includes a polemic issue with many legal and medical implications: doping in chess playing. Pharmacological products and a variety of new drugs appear to improve cognitive functioning in attention, memory, learning, and executive functions (Fond et al., 2015; Repantis et al., 2010). Several substances, such as stimulants, narcotics, anabolic agents, diuretics, and peptide and glycoprotein hormones and their analogues, are prohibited in a variety of sports, such as athletics, cycling, soccer, and swimming. In contrast to physical performance, however, doping effects appear to be far more complex regarding cognitive performance. In the paradigmatic domain of chess, the effect of potential pharmacological enhancers is, apparently, unwarranted (Mihailov & Savulescu, 2018).

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psychophysiology and brain functioning

Nevertheless, the World Chess Federation (FIDE) adopted a drug policy in 1999, and oversees doping controls during major chess tournaments. A recent review has suggested that an improvement in brain performance in chess playing may be achieved with increments in the O2 supply by therapy with erythropoietin (EPO), increases of body glycogen by therapy with insulin, or with mental stimulation by caffeine. In addition, androgenic-anabolic substances, amphetamines, nicotine, and cocaine appear to exert innocuous effects on the quality of chess playing (Golf, 2015b). On the other hand, some steroids and hormones have positive effects on cognition only when present in natural concentrations. Besides, pharmaceutical preparations show positive effects only at low baseline cognition, whereas these hormones present negative effects on mental cognition at elevated concentrations. For example, a randomized controlled trial with thirty-nine chess players who were administered modafinil, methylphenidate, caffeine, or a placebo suggests that these substances do improve decision-making, albeit performance worsened notably with time constraints (Franke et al., 2017).

5.2 Brain Basics The brain is an intriguing organ. Brain anatomy and brain structures and functioning are certainly complex, with between 150 and 200 highly interconnected cortical areas. In addition, there is a high degree of inter-individual variability in these structures and functions, and several notable brain interhemispheric differences. A number of human brain atlases with microstructure data and cortical segregation tools have been developed to explore what is probably one of the fundamental frontiers of scientific knowledge (Amunts & Zilles, 2015). In sharp contrast to other species, the cerebral cortex is the most recent brain structure to have evolved in humans, underlying the anatomical basis of cognitive abilities (Rakic, 2009). The cerebral cortex governs several properties and functions closely related to chess performance, such as perception, memory, and higher-level abstract skills, such as concentration, reasoning, and thinking. The brain is divided into four main lobes in the right and left brain hemispheres: frontal, parietal, temporal, and occipital (Clark, Boutros, & Mendez, 2010; Hill & Schneider, 2006). The frontal lobes control motor skills, including voluntary movement and speech, and intellectual and behavioural functions particularly important for chess, such as problem solving and judgement. The parietal lobes involve sensory awareness, symbolic communication, and abstract reasoning. The occipital lobes operate the visual-processing system. The temporal lobes are implicated in visual memory and in the recognition of objects and faces, and in verbal memory for the use of language. These are only the main basic functions of the brain lobes, as there is a high degree of interactions within and across these main brain regions. For

brain basics

61

example, the neural reuse theory provides an alternative approach concerning the organization of brain modules and the localization of cognitive functions (Anderson, 2010). Brain white matter is a densely packed assembly of myelinated projections of neurons, whereas brain grey matter is composed of the cell bodies of neurons. White matter seals the four lobes together and provides the connectivity among the four regions into specific networks designed to execute a variety of mental operations. In addition, ridges (gyri) and grooves (sulci) characterize the surface of the cerebral cortex. Deeper sulci are also termed fissures, with the most remarkable one being the inter-hemispheric fissure, which separates the two brain hemispheres. The Figure 5.1 (a) shows the four main lobes of the human cerebral cortex: frontal, parietal, temporal, and occipital. The study and direct in vivo observation of the brain has experienced a considerable expansion during the last few decades because of the growing availability of sophisticated techniques. These permit the study of what is going on in the brain in a diversity of circumstances (Volkow, Rosen, & Farde, 1997), (a)

(b) NZ

Frontal Lobe

F9 F10 F7 F5 F3 F1 F2 F4F6 F8

Parietal Lobe T9

Temporal Lobe

Occipital Lobe

T10 T7

P9

P7

T8 P5 P3

O1

P1 P2 P4

OZ IZ

P6

P8 P10

O2

Figure 5.1 Diagram (a): the four main lobes of the human cerebral cortex: frontal, parietal, temporal, and occipital. The main functions of the cerebral cortex are (frontal lobes): motor skills, voluntary movement, speech, problem solving and judgement; (parietal lobes): sensory awareness, symbolic communication, and abstract reasoning; (occipital lobes): visual processing; (temporal lobes): visual memory, recognition of objects and faces, and verbal memory for the use of language (reproduced with permission from the American Psychological Association). Diagram (b): the 10–20 system for the recording of electroencephalograms (EEGs) in humans, showing the reference electrodes nasion (NZ) and inion (IZ), and electrodes corresponding to the cerebral cortex lobes, frontal (F), temporal (T), parietal (P), and occipital (O); the amount of electrodes can vary depending on the research aims and kind of equipment

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psychophysiology and brain functioning

including those involved in chess playing and chess expert performance and acquisition. The study of the brain functioning of chess players can be classified into two main research streams. The first stream deals with electroencephalograph. EEG was the very first method used to analyse brain activity, and it probably remains the cheapest and most used nowadays. The second stream comprises other brain-imaging techniques, and also incorporates some of the general findings obtained with EEG. In general, brain activity in chess players has been observed to vary in accordance with the brain region being analysed together with the level of chess expertise.

5.3 Electroencephalography (EEG) EEG is a widely used technique applied to the measurement, recording, and representation of the brain’s activity. It is an electrical biosignal produced by aggregated electric potential differences elicited from neuronal activity. This signal is obtained with computer hardware and software, which includes the standard 10–20 system recording cap placed on the scalp of the subject (see diagram (b) in Figure 5.1). Each electrode is designated by letters and numbers that identify the position in the names of the main brain lobes (Acharya et al., 2016). The EEG amplitude (voltage) varies between 1 and 100 μV in a normal healthy adult depending on the stimulation and the subject’s mental state. Different frequency bands characterize EEG in different brain states. Higher frequencies imply a higher level of brain activity. For example, the delta band (from 0.1 to 3 Hz) relates to an unconscious state such as sleep, the alpha band (from 8 to 12 Hz) relates to a relaxed but conscious state, and the gamma band (from 30 to 100 Hz) relates to motor functions and a higher mental activity (Carretié, 2001). EEG has a high temporal resolution and comprises studies in three broad areas: spontaneous brain activity, single-neuron bioelectric events, and event-related potentials (ERPs). The ERP application is the most commonly used in experimental psychology studies, with the main focus being placed on mental processes such as perception, attention, language processing, memory, and decision-making. The ERP application aims to detect the brain’s electrical activity in response to diverse physical stimuli when associated with mental activity or in preparation for specific actions. For example, two classical ERP components are the N200 and P300 negative deviations (N), appearing between 185 and 325 milliseconds after the onset of an auditory or visual stimulus, whereas positive deviations appear between 300 and 400 milliseconds afterwards. Both components have been consistently linked with perceptual and attention cognitive processes (Patel & Azzam, 2005). Individual differences in relevant constructs for chess performance relate to EEG, such as semantic memory and the ability to learn new material (Doppelmayr et al., 2002), general creativity (Dietrich & Kanso,

electroencephalography (eeg)

63

2010) and verbal creativity (Fink & Neubauer, 2006), and mental arithmetic tasks (Duru & Assem, 2018; Garach et al., 2015). EEG is a complex technique that is highly demanding, both technically and computationally (Kenemans, 2013; Weiergräber et al., 2016). Therefore, some studies with chess players focus on the evaluation of EEG data analysis techniques, such as the Higuchi fractal dimension, with non-linear methods (Stepien, Klonowski, & Suvorov, 2015). Research more substantially linked to the brain activity of chess players has addressed more specific hypothesis. For instance, the EEG theta Fz/alpha Pz ratio was used as an estimation of the brain load at pre-game, chess game, and post-game stages with a 2550 Elo rating points elite chess player (Fuentes et al., 2018). As expected, the brain load was higher with the greater demand of information processing during the chess game stage. A key finding, however, was the higher activation in the prefrontal cortex at the pre-game stage. The brain load at the next game stage was anticipated analogously to the association of testosterone levels with winning a chess contest before it actually takes place (Mazur et al., 1992). This singlesubject study design precluded further explanations as to how individual differences in chess expertise could modulate this behaviour, however. Individual differences between expert and novice chess players during EEG recordings have also been reported by using recognition tasks of chess information. Eight high-proficiency chess players compared with eight low-proficiency chess players underlined significant differences when eye-tracking chessboards comprising five differentiated conditions: piece positioning, check situations, checkmate situations, checkmate in one move, and capturing pieces (SilvaJunior et al., 2018). High-proficiency players fixed their eyes on relevant parts of the position with more EEG activation in brain areas related to planning and decision-making, such as the prefrontal cortex. In contrast, low-proficiency players fixed their eyes on larger spaces, implying the processing of a greater amount of information, with more brain activity in areas related to the primary processing of vision and eye control, such as the occipital and parietal lobes. These findings are somewhat aligned with the idea that prefrontal cortex activation might be particularly relevant for more proficient individuals when working with associative relationships, and planning (Clark et al., 2010). Another study exposed eleven expert and eleven novice chess players to four kinds of recognition tasks: whether there was a white king on the board, whether or not the black king was in check, whether or not the black king was checkmated, and whether or not a specified chess piece could checkmate the black king in the next move (Volke et al., 2002). The study examined the degree of coherence – i.e., the extent of the relationships between different cortical areas in resolving the given tasks. Experts showed well-mastered task resolution and automatic performance (i.e., high coherence), whereas novices showed poorly mastered task resolution (i.e., low coherence). Recognition stimuli have also been used to examine individual differences between chess

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experts and novices in the N200 and P300 EEG components (Wright et al., 2013). Fourteen expert chess players and fourteen novice chess players attempted to recognize a check position, the presence of a black knight, a non-check position, and the absence of a black knight. Expert players had a more pronounced N200 in the check tasks and a larger P300 in the knight tasks compared to novices, suggesting a better harmonization of perceptual inputs into memory – i.e., superior pattern recognition and chunk retrieval by experts over novices. These findings support consistent individual differences between experts and novices in information processing, providing additional support for the template theory of expert memory. Further research has analysed a compelling hypothesis of intelligence with data from chess players. The neural efficiency hypothesis (NEH) maintains that individual differences in intelligence relate to individual differences regarding brain activation during cognitive tasks. More specifically, the NEH predicts that, when confronted with a relatively demanding cognitive task, people who are more intelligent tend to display lower brain activation, whereas people who are less intelligent tend to display higher brain activation (Neubauer & Fink, 2009a). Alpha band event-related desynchronization (ERD) is a valid EEG method to characterize the degree and topographical distribution of cortical activation in addressing the NEH. The ERD posits that the alpha EEG band within 7.5 and 12.5 Hz changes during cognitive activity. Decreases in ERD are taken as increased neural excitability and cortical activity, whereas increases in ERD are taken as decreased neural excitability and cortical inactivity. This paradigm was applied to fifty-five people from the general population in experimental tasks involving short-term and working memory, and attention switching in the central executive task (Grabner et al., 2004). Overall, the NEH was supported to a greater degree for fluid as opposed to crystallized intelligence, for males compared with females, and regarding the interaction of type of task with brain area by sex. There were positive associations of fluid intelligence with ERD for males in the frontal lobe when performing the central executive task. The ERD method was also applied to another sizable sample of forty-seven chess players involving mental speed, memory, and reasoning tasks (Grabner, Neubauer, & Stern, 2006). This experiment compared in addition the association of both intelligence and chess skill with the elicited cortical activation pattern. These latter ERD findings with the chess sample were surprisingly similar to those findings obtained from the study with the non-chess sample. In accordance with the NEH, individuals who scored higher in cognitive ability had lower brain activity than individuals who scored lower in cognitive ability throughout the three experimental tasks. Furthermore, the activation of the prefrontal brain cortex was more efficient in individuals scoring higher in cognitive ability. When taking into account the level of chess skill and concerning the short-term memory and reasoning tasks, chess players with a

overview of brain-imaging studies

65

higher level of chess skill had lower activation of the frontal cortices, albeit higher activation of the parietal cortices. In contrast, more skilled players also displayed higher cortical activation than less skilled players during the memory task, in virtually all brain areas. This finding was attributed to the manipulation of verbal-semantic information during memory tasks, which might indeed reflect higher efficiency in mobilizing prior knowledge resources. Overall, the main picture of the studies addressing the NEH underline the remarkable individual differences in brain activation, but also in intelligence and chess skill level, with brighter players displaying higher efficiency in brain functioning.

5.4 Overview of Brain-Imaging Studies Brain-functioning study techniques tend to be costly, require accurate execution, and impose severe and intensive computational requirements. Nonetheless, the number of brain-imaging studies with chess players and experts in several fields has experienced progressive growth in the past few years. A recent comprehensive investigation scrutinizes individual differences between experts and novices from a neuroimaging approach, in domains such as chess, mental calculation, and perceptual and motor expertise in several occupations (Bilalić, 2017). Table 5.1 shows an overview of most of the twentysix brain-imaging studies performed with chess players, summarizing the characteristics of the sample, the kinds of tasks performed during brain scanning, the brain-imaging method, the brain areas and structures being analysed, and the main basic findings. The sample size ranged from a single chess player (Fuentes et al., 2018) to forty-seven chess players (Grabner et al., 2006), with a mean sample size of sixteen chess players (Sd = 11). Over 90% of the participants in these studies were males. Furthermore, several studies compared a group of experts against a group of novice chess players, whereas only nine studies (36%) did not conduct such kind of comparison. Most studies considered the Elo rating as the index by which to separate experts from novices, even though some studies applied an independent test to either classify or verify the level of chess skill of the participants (Silva-Junior et al., 2018; Volke et al., 2002; Wright et al., 2013). All the studies used visual stimuli during chess playing, chess problem solving, and memory or recognition tasks. One study used only verbal stimuli within a blindfold chess paradigm (Saariluoma et al., 2004). There were five main kinds of behavioural tasks or paradigms applied to each study: playing a chess game against a computer, solving chess positions, recognizing chess positions, memorizing chess positions, and completing self-report questionnaires. In some studies, two or more of these tasks were combined into a single experimental paradigm. Moreover, a few studies also included non-chess aspects, such as face, scene and object recognition, or theory of mind and empathizing tasks (Bilalić, Langner, et al., 2011; Krawczyk et al., 2011; Powell

Table 5.1 Studies in brain functioning in chess players (EEG = electroencephalography; MEG = magnetoencephalography; fMRI = functional magnetic resonance imaging; PET = positron emission tomography; SPECT = single-photon emission computerized tomography). In the N column, ‘M’ denotes that all participants were males, and ‘F’ denotes the number of females N

(Amidzic, Riehle, & Elbert, 2006)

10 experts (2400 ~ 2600) Chess game against a MEG (gamma-band Medial temporal There are more frequent 10 novices (> 1700) computer activity, 20 – 40 Hz) lobes; frontal and focal gamma bursts in (M) parietal cortex; deeper structures of the hippocampus medial temporal lobes of amateur players. There are more frequent gamma bursts in the frontal lobes of chess grandmasters. 10 experts (2400 ~ 2600) Chess game against a MEG (gamma-band Medial temporal Amateur players show 10 novices (> 1700) computer activity, 20 – 40 Hz) lobe; frontal and higher activity in the (M) parietal cortices medial temporal lobe. Grandmasters show more activity in the frontal and parietal cortices.

(Amidzic et al., 2001)

Tasks/paradigm

Method

Main brain areas/ structures

Study

Main conclusion(s)

(Atherton et 7 novices al., 2003) (M)

Solve chess positions fMRI (14 ~ 16 sagittal Superior frontal slices) lobes; parietal lobes; occipital lobes; left hemisphere

(Bilalić et al., 8 experts (> 2000) 2010) 15 novices (M)

Recognition of chess fMRI (176 sagittal positions slices)

Occipito-temporal junction

Bilateral activation is revealed in the superior frontal, parietal, and occipital lobes. Small areas of activation are observed unilaterally in the left hemisphere. The left hemisphere shows more activation than the right. Experts’ superiority in object recognition relates to bilateral activity next to the occipito-temporal junction.

Table 5.1 Cont. Study

N

Tasks/paradigm

Method

(Bilalić, Kiesel, et al., 2011)

8 experts (~ 2130) 8 novices (M)

Geometric task; identity task; check task; eye movements

fMRI (176 sagittal slices)

(Bilalić, Langner, et al., 2011)

7 experts (~ 2100) 8 novices (M)

Recognition of faces fMRI (176 sagittal and chess slices) positions

Main brain areas/ structures

Main conclusion(s)

Temporal gyrus; Left temporal and parietal occipito-temporal areas along the dorsal junction; parietostream relate to chessoccipito-temporal specific object recognijunction; supration. Only in experts are marginal gyrus homologous areas on the right hemisphere also engaged in chessspecific object recognition. Fusiform face area Experts’ FFAs are more (FFA) activated than those of novices with naturalistic full-board chess positions and with randomly disturbed chess positions.

(Bilalić et al., 8 experts (~ 2100) 2012) 15 novices (M)

Recognition of chess fMRI (176 sagittal position slices)

(Campitelli, Gobet, & Parker, 2005)

Memorizing chess positions

2 experts (2550, 2450) 12 novices (?)

fMRI (22 coronal slices)

Dorsal stream; pos- Experts’ superior recogniterior temporal; tion performance and left inferior partheir functions arise in ietal lobe; collatbilateral posterior temeral sulci; poral areas and the left bilateral inferior parietal lobe. retrosplenial The bilateral collateral sulci, together with the bilateral retrosplenial cortex, are more sensitive to normal than random positions among experts. Frontal lobes; pos- There is brain activation terior cingulate; in the frontal areas of cerebellum the novices but not in the experts, who, rather, use from anterior to posterior areas of the brain.

Table 5.1 Cont. Study

N

Tasks/paradigm

Method

(Campitelli et al., 2007)

5 players (~ 1971) (?)

Memorizing chess fMRI (22 coronal positions; slices) recognition of chess positions

(Campitelli et al., 2008)

2 experts (2550, 2500) (?)

Memorizing chess positions

fMRI (22 coronal slices)

Main brain areas/ structures Temporal lobes; frontal and parietal lobes

Main conclusion(s)

The working memory tasks activate frontal and parietal lobes. Long-term memory tasks activate temporal areas. Left temporoThe study finds a similar parietal junction; left-lateralized pattern left frontal areas of brain activity in both masters. The brain areas activated are the left temporo-parietal junction and left frontal areas.

(Duan et al., 15 experts (2200 ~ 2600) Raven’s Standard 2012) 15 novices Progressive (F = 6 experts, 6 Matrices novices)

(Fuentes et al., 2018)

1 expert (2550) (M)

fMRI (176 sagittal slices)

Chess game against a EEG (theta Fz/alpha computer Pz)

Caudate nucleus

Prefrontal cortex

Long-term chess training relates to smaller caudate nuclei, enhancing better integration of cognitive skill acquisition, in accordance with the default model network. Cortical theta Fz/alpha Pz ratio arousal increases and heart rate variability decreases during a chess game. The brain load increases during the chess game. There is pre-activation in a pregame measure. The prefrontal cortex might be preparatorily activated.

Table 5.1 Cont. Tasks/paradigm

Method

Main brain areas/ structures

Study

N

(Grabner et al., 2006)

Parietal cortices; • 47 experts (1325 ~ Personality (NEO- EEG (event-related FFI); state anxiety desynchronization; frontal cortices 2338) (STAI); upper alpha band) • 23 high (~ 2076) Intelligenz• 24 low (~ 1717) Struktur-Test • (M) 2000; speed task (ST); memorizing chess positions; solving chess positions

(Hanggi et al., 2014)

20 experts (~ 2366) 20 non-players (M)

Fluid intelligence; MRI (160 sagittal visuospatial abilities slices)

Main conclusion(s)

Intelligence and chess expertise have different impacts on neural efficiency. More skilled chess players display higher activation over the parietal cortices and lower activation over the frontal cortices in the speed and reasoning tasks. Caudate nucleus; Grey matter volume and precuneus; cortical thickness are occipito-temporal reduced in chess players junction (OTJ) compared with controls in the OTJ and precuneus. There are no differences in the volume of the caudate nucleus.

(Krawczyk et 6 experts (~ 2515) al., 2011) 6 novices (M)

Memorizing chess positions, faces, scenes, objects

fMRI (tilted axial slices: 3 mm thick, 0.5 mm slice gap)

(Li et al., 2015)

Age, sex, education, weight, handedness, mental and physical illness; Raven’s Standard Progressive Matrices

MRI (176 sagittal slices)

29 experts (~ 2401) 29 novices (F = 9 experts, 15 novices)

Fusiform face area; Chess configurations are cingulate cortex not strongly processed by face-selective regions. Areas in the posterior cingulate and right temporal cortex are more active in experts. The posterior cingulate cortex is responsive to chess only in experts. – A multimodal MRI dataset.

Table 5.1 Cont. Study

N

Tasks/paradigm

Method

(Nichelli et al., 1994)

10 (M)

Recognition of chess PET positions; solving chess positions

Main brain areas/ structures

Main conclusion(s)

Parieto-occipital Solving a complex problobe junction; lem requires the activity left middle temof a network of several poral gyrus; left interrelated, but funcsuperior pretionally distinct, ceremotor cortex; bral areas. superior parietal lobe; medial superior parietal cortex; hippocampus; occipital-parietal junction; left orbitofrontal cortex; right prefrontal cortex

(Onofrj et al., 1995)

5 (1800 – 2200) (M)

Single chess position SPECT solving

Frontal lobe

(Powell, et al., 2017)

12 novices (M)

Theory of mind (ToM) task; empathizing task; solving chess positions

Temporo-parietal junction; superior temporal gyrus; posterior cingulate gyrus

fMRI (176 sagittal slices)

The non-dominant frontal lobe is active in the brain of chess experts when elaborating a solution for a complex chess problem. The chunking of elements into meaningful groupings and parsing of visual stimuli are functions of the nondominant hemisphere. ToM and empathy tasks activate the righthemisphere orbitofrontal cortex and bilateral middle temporal gyrus. Chess tasks activate the medial-frontal and parietal cortex. Both areas overlap to a certain degree.

Table 5.1 Cont. Study

N

Tasks/paradigm

Method

(Rennig et al., 2013)

Data reanalysed from past studies (Bilalić et al., 2010, 2011, 2012) (M)

Recognition of chess fMRI (176 sagittal positions slices)

Main brain areas/ structures Temporo-parietal junction

Main conclusion(s) There is higher activation of the temporo-parietal junction in experts compared with novice players when presented with complex chess positions, suggesting that experts have higher visual integration skills.

(Saariluoma et al., 2004)

6 (~ 2084) (M)

Blindfold chess tasks PET (memory and problem solving)

Temporal lobe; frontal lobe

The memory task activates temporal areas; the problem-solving task activates frontal areas. Expert players process chess images differently from ordinary images. Visuospatial representations are characterized by large learned chunks and automated processing habits.

Table 5.1 Cont. Study

N

(Silva-Junior 8 high-proficiency et al., 8 low-proficiency 2018) (?)

Tasks/paradigm

Method

Solving chess positions

EEG (entropy analyses, factor analyses)

Main brain areas/ structures Prefrontal cortex; occipital lobe; parietal lobe; temporal lobe

Main conclusion(s) High-proficiency players present brain activation in areas related to planning and decisionmaking, such as the prefrontal cortex. Lowproficiency players show more brain activity in visual-processing areas, such as the occipital and parietal, or in areas related to eye control, such as temporal lobe association areas.

(Stepien, Klonowski, & Suvorov, 2015)

3 experts (M)

(Volke et al., 11 high-proficiency 2002) 11 low-proficiency (M)

Chess game against a EEG (Higuchi fractal computer dimension; empirical mode decomposition)

–

Recognition of chess EEG (coherence) positions Solving chess positions

Frontal lobe; prefrontal cortex

The Higuchi fractal dimension is a better method for the analysis of EEG signals related to chess tasks than that of sliding window empirical mode decomposition. Experts show wellmastered and automatic performance (high coherence), whereas novices show poorly mastered task resolution (low coherence).

Table 5.1 Cont. Study

N

Tasks/paradigm

Method

(Wright et al., 2013)

14 experts (1650 – 2450) 14 novices (M)

Recognition of chess EEG (N200, P300) positions

Main brain areas/ structures Frontal lobe

Main conclusion(s) Expert–novice differences in posterior N200 begins early on checkrelated searches (240 ms). Prolonged N200 components reflect the matching of current perceptual input to memory, highlighting experts’ superior pattern recognition and memory retrieval of chunks.

cerebral cortex areas

81

et al., 2017). Regarding the brain-imaging method, fMRI and EEG were the most usual applications of choice, with eleven and six studies (44% and 24%), respectively. Two studies used MEG, PET, or MRI (8%), and only one study applied the SPECT method (4%). The activity in most cerebral cortex areas and other brain structures was meaningfully related to the performance in the experimental tasks conducted in this set of studies. The frontal lobe was the brain area yielding the most interesting and remarkable findings independently of the applied method, however. The presentation of the main findings from this body of research is structured into the following four sections: cerebral cortex areas, hemispheric specialization, other brain areas and anatomical changes, and summarizing findings about brain functioning and chess.

5.5 Cerebral Cortex Areas Prominent differences in the activation of the cerebral cortex areas between expert and novice chess players and in other domains emerge systematically (Bilalić, 2017). These differences have been mainly associated with working memory and long-term memory. For example, a review of PET and fMRI studies about expert memory when executing working-memory tasks highlights that the acquisition of expertise might run through a two-stage brain functional reorganization process (Guida et al., 2012). This reorganization process is here understood as the reallocation of brain resources occurring during expert acquisition from working memory to long-term memory. The studies with experts demonstrate brain activation of areas involved in longterm memory tasks, which suggests compatibility with functional brain reorganization. In contrast, the studies with novices demonstrate that there was brain deactivation of areas involved in working memory tasks, which suggests incompatibility with functional reorganization. This dual process is attributed to more practice through the acquisition of expertise. In this view, it is argued that the reorganization process contributes to increasing the size of the chunks, which would be stored in long-term memory, eventually leading to the consolidation of higher-level knowledge structures. Additional fMRI studies with chess tasks requiring the use of memory have also underlined meaningful differences between the brain functioning of experts and novice chess players. For example, a study comparing two expert players with twelve novice players in the memorization of typical chess positions reports that novice players tend to use frontal lobe areas, whereas, in contrast, expert players use from anterior to posterior areas of the brain (Campitelli et al., 2005). Another study with five expert players informs that frontal and parietal brain areas are activated in working-memory tasks, whereas temporal areas are activated in long-term memory tasks (Campitelli et al., 2007). These findings support the view that chess players

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employ long-term memory chunks, which are purportedly stored in the temporal lobes (Gobet & Simon, 1996c). Furthermore, the advantage of experts over novice players is highly consistent in the recognition of chess positions regarding the brain activity next to the occipito-temporal junction (Bilalić et al., 2010), and posterior temporal and left inferior parietal lobes. Moreover, the collateral sulci and retrosplenial cortex have also been shown to be more sensitive among experts than among novices (Bilalić et al., 2012). These latter findings about the recognition of chess objects and their interrelationships evidence the extensive knowledge of expert players about specific chess patterns. The performance in recognizing chess patterns drops meaningfully with the randomization of meaningless chess positions, however. Furthermore, experts use the same regions as novices do when recognizing chess objects, though experts may also use additional brain regions. There appears to be, therefore, a learning process, whereby experts would be at advanced stages of learning, whereas novices might be at earlier stages of learning. Further reanalyses of some of these fMRI studies have focused on the temporo-parietal junction, a multimodal sensory brain area with a principal role in the social brain (Rennig et al., 2013). This brain area is more activated in expert than in novice players when exposed to complex chess positions, suggesting higher visual integration skill on the part of experts vis-àvis novices. Other differential activation patterns between expert and novice chess players, mainly located in the frontal and temporal cerebral areas, have also been found employing other brain-imaging techniques, such as EEG, fMRI, or PET. For example, EEG findings indicate that better performers show brain activation in the prefrontal cortex, whereas worse performers show brain activation in visual-processing brain areas, such as the temporal, occipital, and parietal areas, during a chess problem-solving task (Silva-Junior et al., 2018). Similarly, there is support for the neural efficiency hypothesis when analysing the brain activity of a considerable group of chess players (Grabner et al., 2006). Higher-skilled players show a lower level of activation in the frontal cortices but a higher level of activation in the parietal cortices when compared with lower-skilled players in short-term memory and reasoning tasks. A particularly attractive technique is that involving focal gamma bursts obtained with the MEG technique. The oscillatory neural activity in the gamma frequency band (30 to 100 Hz) appears at early stages less than 150 ms after stimuli onset and at later stages more than 200 ms after stimuli onset. This signal is particularly noteworthy for the cognitive processes involved in chess playing, because it implies several cognitive properties that are useful in chess. It has been consistently linked with attention and perceptual processes, motor tasks, short- and long-term memory, and problem solving (Rieder et al., 2011). Furthermore, it has also been associated with more specific cognitive functions such as object representation, memory and language processes,

hemispheric specialization

83

visual awareness, and for the performance in memory tasks implying subsequent recognition. In addition, the match-and-utilization model (MUM) attempts to explain the gamma-band oscillation in terms of two main processes: comparing memory material with the stimuli, and the utilization of signals obtained from this comparison (Herrmann, Fründ, & Lenz, 2010). The gamma-band activity predominates in different cortical areas when contrasting expert with novice chess players. Two studies report that focal gamma bursts were more frequently observed in the frontal and parietal lobes of chess grandmasters, whereas, in contrast, focal gamma bursts were more frequently observed in the deeper structures of the medial temporal lobes of novice chess players (Amidzic et al., 2006, 2001). These findings are interpreted in accordance with memory formation in novice chess players. The medial temporal lobe might play a transitional role during the creation of expert memory. In this view, expert chess players recall stored information from long-term memory, whereas novice chess players need to encode the new information. This discrepancy is argued as supportive of the theory regarding the extensive repository of chunks stored in experts’ long-term memory – i.e., templates. In blindfold chess, looking at the pieces on the board is not allowed, and the opponent’s moves are transmitted verbally; hence, blindfold chess is particularly appealing for examining taxing brain functions involving memory and problem solving. The demanding task of blindfold chess was examined with the PET method (Saariluoma et al., 2004). Different tasks elicited the activation of different cerebral cortex areas. A memory task activated temporal areas, whereas a problem-solving task activated frontal areas. These findings uphold the notion that the visual representations of expert players were guided by learned chunks of chess information, and by highly automated informationprocessing habits. Bearing in mind the severe restriction imposed by the blindfold chess paradigm, these outcomes support the view that chess-related visual information is probably represented in the brain in a quite different way from regular images because of the previously learned visuospatial chunks, which might be automatized to a great extent and retrieved from long-term memory.

5.6 Hemispheric Specialization Crucial qualities of the human brain are cerebral lateralization and hemispheric specialization. The left hemisphere dominates linguistic functioning in most people, whereas the right hemisphere is more important in the experience and expression of emotions (Clark et al., 2010). Some studies examining the brain functioning of chess players have addressed different aspects of the hemispheric specialization issue. For example, a dividedvisual-field experiment about accuracy performance and reaction time

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highlights brain hemispheric specialization regarding the perceptual organization of chess information (Chabris & Hamilton, 1992). Within this paradigm, there should be a right hemisphere advantage for single-chunk fragments of chess information, whereas there should be a left hemisphere advantage for multiplechunk fragments of chess information. The findings from sixteen right-handed master-level chess players indeed suggest that the right hemisphere is more efficient at identifying chess positions with a single chunk configuration, while the left hemisphere is more efficient at identifying chess positions with multiplechunk configurations. Because of the right hemisphere specialization concerning complex visuospatial tasks, these findings support the notion of the superiority of the right hemisphere at learning chess chunking rules. These latter findings also parallel the outcomes from an fMRI study with just two right-handed grandmaster players, whereby the left temporo-parietal and left frontal areas were activated when confronted with an autobiographical memory task (Campitelli et al., 2008). That both players displayed such analogous left brain hemisphere lateralization corroborates the superiority of expert over novice players at recovering chess chunks and in pattern recognition, which was additionally substantiated by EEG findings (Wright et al., 2013). Furthermore, the larger amount of knowledge gained by experts over novices has been argued to be the main underlying factor of the principle of the ‘double take’ of expertise (Bilalić, 2017, 2018). In accordance with this principle, the crucial neural difference between experts and novices is that, although both groups activate similar brain areas in executing a cognitive task, experts tend to activate additional homologous areas in the opposite brain hemisphere. Higher left hemisphere activation has also been found with novice players when solving chess positions (Atherton et al., 2003). This fMRI finding was detected mainly in the occipital and parietal lobes, however. In contrast, the frontal lobes were unusually deactivated, suggesting that certain problemsolving skills implicated in chess would depend on cerebral cortex areas other than the lateral prefrontal cortex, and particularly anticipated at lower levels of chess skill. Furthermore, the SPECT study carried out with five expert players highlights the importance of the dorsal prefrontal and middle temporal lobes in the non-dominant hemisphere for chess skill: the right hemisphere for four right-handed players, and the left hemisphere for the one left-handed player (Onofrj et al., 1995). The hemispheric non-dominant frontal lobe, and to a lesser extent the temporal lobe, were activated when attempting to find a solution for a complex chess problem, suggesting that the chunking of chess elements into meaningful patterns and parsing of visual stimuli are functions governed by areas located in the non-dominant brain hemisphere. Additional fMRI findings suggest that left hemispheric temporal and parietal areas activated when recognizing chess-specific objects are also activated in the right hemisphere only for experts (Bilalić, Kiesel, et al., 2011).

other brain areas and anatomical changes

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5.7 Other Brain Areas and Anatomical Changes Sophisticated brain-imaging techniques allow us to examine other brain structures and functions. One such structure is the fusiform face area (FFA), a visual area located in the temporal lobe that is activated even at extremely young ages when viewing faces (Clark et al., 2010). The FFA is also activated when exposed to objects entailing a certain experience for the individual, such as birds for an ornithologist (Bukach, Gauthier, & Tarr, 2006). The FFA was analysed with seven chess experts and eight chess novices through the fMRI technique by contrasting the recognition of faces and chess positions (Bilalić, Langner, et al., 2011). In the recognition of both kinds of objects, the FFA of experts was more activated than that of novices when viewing both coherent chess positions and randomly disrupted positions. These findings support the view that the specific nature of the objects within a given expert domain might modulate the FFA’s activity. In addition, contrasting the recognition of faces, scenes, objects, and chessboards was investigated in another fMRI study by comparing six experts with six novice chess players. This study involved the analyses of brain regions involved in the processing of faces and chess configurations, to ascertain whether the perception of both kinds of objects activates common brain regions (Krawczyk et al., 2011). The main findings in this study suggest that face and chess processing occurs independently. Face-processing areas such as the FFA are disengaged from the processing of chess stimuli. For example, a notable activated brain area in the expert players was the posterior cingulate cortex, corroborating the memory retrieval and thinking requirements during the performance of chess tasks, as reported elsewhere (Campitelli et al., 2007). Brain areas related to the theory of mind (ToM), such as the temporoparietal junction, superior temporal gyrus, and posterior cingulate gyrus, have also been examined in relation to chess playing (Powell et al., 2017). ToM is the ability to understand and predict the mental state of other people, including emotions, desires, and intentions. This attribute may be quite important in chess playing when attempting to anticipate the tactical and strategic plans of the opponent. Twelve novice players were exposed to ToM, empathy, and chess-problem-solving tasks while their brain activity was recorded with fMRI. Brain areas involved in ToM were mainly activated with ToM and empathy tasks, whereas cortical areas in the medial frontal and parietal lobes were activated in turn with chess tasks. A certain degree of neural overlap between both processes is also reported in this study, however. Making decisions about potential chess moves intertwined with ToM considerations such as reasoning iteratively about the opponent’s moves. Another intriguing feature concerning the inter-individual variability between chess player’s brains is concerned with whether there are brain anatomical changes associated with the level of chess skill. Anatomical changes

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have been reported to occur in two complex brain structures, the precuneus and the caudate nucleus. The precuneus is located in the superior parietal lobe. This structure exhibits alternate connections with the frontal lobe and is involved with functions such as consciousness, body movements, self-awareness, episodic memory retrieval, and visuospatial imagery. The caudate nucleus is located in the basal ganglia. This is a group of grey matter nuclei at the base of the brain hemispheres closely related to the frontal lobes in the acquisition and expression of cognition. The caudate nucleus plays a crucial role, for instance, in the serial order of movements and behaviour (Clark et al., 2010). Both the precuneus and the caudate nucleus have been linked with the search and generation of moves in professional players of shogi, a Japanese game sharing many characteristics with conventional chess (Wan et al., 2011). Regarding the anatomical changes in both structures in chess players, the caudate nuclei are reported as being meaningfully smaller in expert than in novice players (Duan et al., 2012). Expert players displayed a larger default brain network than novices, however. A default brain network is a concept that encapsulates a group of interconnected brain structures that are active in a baseline resting state, namely the caudate nucleus, the posterior cingulate cortex, and the angular gyrus. These two apparently contradictory findings are interpreted in terms of a synaptic pruning mechanism. The removal of superfluous synapses would contribute to an enhanced and more efficient integration of brain functioning across different brain areas and structures. These findings are partially corroborated in a comprehensive neuroanatomical MRI study with twenty expert chess players compared with twenty non-player controls (Hanggi et al., 2014). This study applied diffusion tensor imaging (DTI) and voxel-based morphometry (VBM) and surface-based morphometry (SBM) techniques to determine the grey matter volumetric characteristics. Grey matter volume in the precuneus and cortical thickness in the occipito-parietal junction were lower in chess players than in control subjects. On the other hand, grey matter volume in the caudate nucleus was very similar in chess players and controls. In accordance with a synaptic pruning mechanism, this outcome is attributed to the earlier starting age for chess playing by the experts involved in the study: between four and fourteen years of age (M = eight years old). Because sensory deprivation during childhood appears to reduce synaptic pruning to a greater extent, stimulation in the chess domain at such young ages might have stimulated a remarkable removal of synapses. This interesting study raises several supplementary questions related to the observed inter-individual variability, however. For example, were the differences in anatomical characteristics the cause or the consequence of becoming involved in chess to the extent of reaching expert level?

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87

5.8 Summarizing Findings about Brain Functioning and Chess The evidence found in this body of research points to the meaningful activation of several areas in the cerebral cortex during a variety of experimental tasks. Brain areas show a notable degree of specialization concerning specific tasks when dealing with chess information. In addition, there are remarkable inter-group differences in brain activity when comparing experts with novice players. For example, diverse anatomical structures and specialized brain areas appear to function as an integrated synchronized network that might be enhanced at higher levels of expertise and chess skill (Nichelli et al., 1994; Volke et al., 2002). Moreover, anticorrelated functional networks may contribute to accounting for these findings. When performing attention and cognitive tasks there are brain areas with increased activity and there are brain areas with decreased activity. Typically, frontal and parietal cerebral lobes areas show increased activity, while the posterior cingulate, medial and lateral parietal, and medial prefrontal cortices show decreased activity. This imbalance grows with progressively more demanding task requirements (Fox et al., 2005). This chapter has addressed the biological underpinnings of chess playing and chess expertise. Psychophysiology and brain activity are fascinating approaches to addressing individual differences using chess as a model domain. Playing chess implies a demanding learning process, and expert chess players reach surprisingly higher performance levels than non-expert players do. This advantage is also reflected in the brain functioning and brain structure of chess players, because there are neuroanatomical and neurophysiological skill adaptations on the part of experts. The body of evidence reviewed in this chapter reflects well six main themes that emerge when explaining how learning a given skill might impinge on substantial observable brain changes (Hill & Schneider, 2006). These six themes are the following: (1) learning is localized and specialized; (2) learning and processing occur in similar brain locations; (3) learning improves processing; (4) some tasks can be reorganized; (5) domain-meaningful stimuli are processed in a special way by experts; and (6) learning produces observable changes. Concerning the specific body of research into the psychophysiology and brain functioning of chess players, there are a few main points that can be singled out for highlighting. 1. Chess experts display different brain activation patterns from novice players. 2. Chess experts appear to be able to integrate more brain areas when dealing with chess-related tasks, such as recognition, memorizing, and problem solving. 3. Expert chess performance implies higher brain hemispheric specialization. Chess experts are more prone to use the non-dominant brain hemisphere than novice players are.

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4. Brain activation and brain structural differences between chess players of different levels of skill could be due to a developmental process because of starting to play chess very early in life, and devoting highly varying periods to studying the extensive knowledge base within the chess domain. 5. There are two main limitations on this body of knowledge. First, the low sample size impairs the statistical power of the studies. Second, most of the samples used in these kinds of studies are males, with an overall male to female ratio (M:F) of 11:1. This disparity may bear a remarkable sex bias, precluding the generalization of these findings to the female population. 6. Moreover, there is a paucity of studies regarding the psychophysiological parameters and hormonal activity of chess players. This relatively unexplored field could be examined in greater depth by incorporating measures of individual differences in a variety of psychological traits related to chess performance. In the light of the current findings concerning the brain functioning of chess players, one question that may be raised is whether chess players are more intelligent than average people are. With better integration of activity in several brain areas, it might be the case that the answer to this question is affirmative. The study of intelligence in chess has yielded inconclusive and sometimes controversial findings, however.

6 Intelligence

Intelligence is probably the most important construct in psychology. Ever since the seminal work at the beginning of the twentieth century suggesting that intelligence is a very general ability, much has been said about human intelligence (Spearman, 1904, 1927). There are several formal models providing a comprehensive account of intelligence, a psychological abstract concept that has important scientific and political implications (Sternberg & Kaufman, 2011). The scores in intelligence tests relate strongly to several variables with a social and practical relevance for daily life. There are robust positive correlations between the intellectual level, measured with psychometric intelligence tests, with work performance, academic achievement, and economic success. Conversely, these correlations tend to be negative with unemployment, delinquency, disease, and mortality. No other psychological variable produces such correlations. The publication in 1994 of the book The Bell Curve elicited a cogent debate in the mass media about human intelligence (Herrnstein & Murray, 1994). This debate was at times driven by significant misinterpretations regarding the extant scientific body of knowledge about human intelligence. Consequently, many scholars and researchers in the field reacted in an attempt to clarify several of the most crucial aspects about human intelligence. For example, the Board of Scientific Affairs (BSA) of the American Psychological Association (APA) encouraged the elaboration of a report about the meaning of test scores and the nature of intelligence (Neisser et al., 1996). This report raised several matters that were unresolved at that time, including the following: 1. the mechanisms by which individual differences in genes contribute to individual differences as measured by psychometric tests, and, to a greater extent, at older ages; 2. the influence of environmental factors in the development of intelligence, particularly of schooling; 3. the role of nutrition; 4. the pattern of the relationships between measures of informationprocessing speed and psychometric intelligence; 5. the progressive and generalized increment of means in intelligence tests in the past fifty years; 89

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6. the differences in mean intelligence test scores between racial groups (i.e., blacks and whites), which are unsupported by either genetic or environmental factors; and 7. the measurement and nature of other constructs akin to intelligence, such as creativity and wisdom. Another similar report around that time highlighted mainstream conclusions concerning the nature, origins, and consequences of individual and group differences in intelligence (Gottfredson, 1997b). Fifty-two experts in intelligence and related fields signed this report, which is structured around six main themes: meaning and measurement; group differences; practical importance; the sources and stability of within-group differences; the sources and stability of between-group differences; and the implications for social policy. Further work has summarized the main opinions when describing the construct of intelligence (Hunt & Carlson, 2007): 1. 2. 3. 4. 5.

intelligence does not exist; intelligence does exist and is measured by intelligence tests; intelligence does exist and is not measured by intelligence tests; intelligence is unchangeable, fixed at birth; intelligence is in part determined by the environment, especially through education; 6. intelligence overlaps with learning ability; 7. intelligence is purely cognitive; and 8. intelligence can take many forms, in domains as diverse as music, mathematics, athletics, and leadership. As with the work by Earl Hunt, the approach taken in this book considers that intelligence can be viewed as the combination of points 2, 5, 6, and 7. Intelligence exists and it can be measured with intelligence tests; it is determined by both genetic and environmental factors; it is intimately related to the ability to learn; and it can be constrained to the cognitive domain. Because the conceptualization and measurement of intelligence has relied on specific tests, several psychometric instruments have been designed to gauge a variety of cognitive abilities. Two desirable properties of intelligence tests are reliability and validity. A test is reliable when it provides the same measurement on different occasions. A test is valid when it measures the construct that it is intended to measure and is predictive of other constructs. In general, tests designed to evaluate cognitive abilities meet both these properties to a large extent. Cognitive abilities tests can be classified in four main ways (Urbina, 2011): (1) examination mode (individual or group); (2) population (children, adults, specific groups); (3) content (verbal, non-verbal); and (4) length (full, abbreviated). Table 6.1 shows an overview of some of the most popular tests to evaluate human cognitive abilities in accordance with the

intelligence

91

Table 6.1 Overview of some tests to evaluate cognitive abilities Test

Reference

Examination Broad factors/subtests

Armed Services Vocational Aptitude Battery (ASVAB)

–

Group

Cognitive Abilities Test (CAT-3)

(Lohman & Group Hagen, 2002) (Naglieri & Individual Das, 1997)

Cognitive Assessment System (CAS) Differential Aptitude Test (DAT-5)

(Bennett, Seashore, & Wesman, 2002)

Group

Fagan Test of Infant Intelligence (FTII)

(Fagan & Individual Detterman, 1992) Kaufman Adolescent and (Kaufman & Individual Adult Intelligence Kaufman, Test (KAIT) 1993) Otis-Lennon Test – Group

Peabody Picture Vocabulary Test (PPVT-4) Raven’s Progressive Matrices

(Dunn & Dunn, 2007) (Raven & Raven, 2008)

General science, arithmetic reasoning, word knowledge, paragraph comprehension, mathematics knowledge, electronics information, auto and shop information, mechanical comprehension, object assembly Verbal, quantitative, non-verbal Planning, attention, simultaneous processing, sequential processing Verbal reasoning, numerical ability, abstract reasoning, mechanical reasoning, space relations, language use Visual recognition memory

Individual

General IQ, crystallized intelligence (Gc), fluid intelligence (Gf) Verbal comprehension, verbal reasoning, figural reasoning, quantitative reasoning Vocabulary ability

Group

General intelligence (g)

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Table 6.1 Cont. Test

Reference

SAT

sat.collegeGroup board.org (Roid, 2003) Individual

Stanford-Binet 5

Examination Broad factors/subtests

Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV)

(Wechsler, 2008)

Individual

Wechsler Intelligence Scale for Children-IV (WISC-IV)

(Wechsler, 2003)

Individual

Wonderlic Personnel Test (WPT)

(Wonderlic & Group Wonderlic, 1992) (Woodcock, Individual McGrew, & Mather, 2001)

Woodcock-Johnson III Test of Cognitive Abilities (WJ III)

Writing, reading, mathematics Fluid reasoning, knowledge, quantitative reasoning, visual-spatial processing, working memory General IQ, verbal comprehension, perceptual reasoning, working memory, processing speed General IQ, verbal comprehension, perceptual reasoning, working memory, processing speed Verbal, arithmetic, and logical questions Achievement tests (22), cognitive tests (20)

Note: The ‘SAT’ acronym initially stood for Scholastic Aptitude Test, though it has been renamed several times. This test is used extensively as part of the college admission process in the United States. examination mode, and lists the cognitive abilities or performances evaluated by each instrument. Some tests comprise several subtests addressing more specific cognitive abilities or performances, such as the ASVAB or the WAISIV. Other tests measure just one broad ability or performance, such as the PPVT-4 or Raven’s Progressive Matrices. A popular score of intelligence conceived in the early twentieth century is the intelligence quotient (IQ), expressed as mental age divided by chronological age (Stern, 1921). The IQ is generally used to provide a quantification of the level of intelligence, which can be readily obtained from several of the tests used to evaluate cognitive abilities. Because intelligence tests are standardized with

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Scoring scale

approaches to the study of intelligence

%

0.13

0.13

13.59

34.13

34.13

13.59

2.14

0.13

IQ

40

55

70

85

100

115

130

145

160

z

-4

-3

-2

-1

0

1

2

3

4

T

10

20

30

40

50

60

70

80

90

CEEB

100

200

300

400

500

600

700

800

900

Figure 6.1 The normal distribution with IQ scores compared with the approximate percentage of cases under the curve, and other scoring systems Notes: % = approximate percentage of cases from the population under different areas of the curve; IQ = intelligence quotient scores; z = standardized scores; T = T scores; CEEB = College Entrance Examination Board.

a representative sample of people, the IQ is usually gauged with an arbitrary mean of 100 IQ points and a standard deviation of 15 IQ points. The IQ follows a normal distribution fairly well, as shown in Figure 6.1. Over 68% of the population falls between one standard deviation below and above the mean, whereas the number of people at both ends of the IQ continuum decreases progressively. Identifying intelligence with the IQ may not be appropriate, however. The IQ is an individual score obtained in a test relative to a broader group of people. In contrast, intelligence is a complex multi-factorial concept with an intricate network of causes and consequences conceived as part of an extensive open system. In this view, intelligence is unobservable; it is, rather, a concept built in accordance with how it is envisaged (Hunt, 2011). For example, the Flynn effect is a remarkable observed phenomenon maintaining that IQ scores in intelligence tests rose over the twentieth century across different cultures (Flynn, 1984, 1987). A striking finding about the Flynn effect, however, suggests that IQ scores measure in fact a correlate that relates weakly to intelligence.

6.1 Approaches to the Study of Intelligence There are several ways to look at what human intelligence means. Historically, diverse theories have been proposed for conceptualizing and accounting for what intelligence refers to. Theories and models about intelligence can be classified into three broad levels of analysis: psychometric, information processing, and

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biological (Hunt, 2011), even though other authors may employ other classification schemes, such as psychometric, physiological, and social (Davidson & Kemp, 2011). Whatever the case, when it comes to investigating the structure, causes, and consequences of human intelligence some empirical studies may approach the study of intelligence from more than one level of analysis. An example could be to examine whether a general intelligence model (psychometric level) predicts the premises posited by the P-FIT model (biological level) concerning brain structure (Colom et al., 2009). Another example could be to analyse whether a measure of general intelligence obtained with Raven’s Progressive Matrices (psychometric level) relates to a reaction time (information-processing level) measure (Jensen & Munro, 1979). Table 6.2 shows the most meaningful theories and models that Table 6.2 Theories and approaches to the study of human intelligence Level

Theory/model/paradigm

Psychometric

Spearman’s g Vernon’s v:ed and k:m Thurstone’s primary mental abilities Guilford’s structure of intellect Fluid (Gf) and crystallized (Gc) intelligence Hierarchical LISREL (HILI) Carroll’s three-stratum Cattell–Horn–Carroll (CHC) g-VPR Planning, attention, simultaneous, successive (PASS) Triarchic theory Multiple intelligences PPIK Emotional intelligence Speed of mental processing (RT, IT) Working memory Verbal comprehension Visual-spatial reasoning Neural efficiency hypothesis (NEH) P-FIT Neural plasticity EDSC

Psychometric extensions/social

Information processing

Biological

Notes: v:ed = verbal, educational; k:m = spatial, practical, mechanical; g-VPR = verbal, perceptual, rotation (manipulation of visual objects); PPIK = intelligence as process, personality, interests, intelligence as knowledge; RT = reaction time; IT = inspection time; P-FIT = parieto-frontal integration theory; EDSC = ecological dominance–social competition.

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95

have been delineated since the beginning of the scientific study of human intelligence. These are classified at four differentiated levels of analysis: psychometric; psychometric extensions or social; information processing; and biological. Theories at the psychometric level are mainly concerned with the structure of human cognitive abilities, relying on a statistical technique known as factor analysis. Factor analysis aims to explain the covariances among several observable measures in terms of a significantly lower amount of latent or unobservable dimensions. When submitting a number of test scores of diverse cognitive abilities to a factor analysis, a recurrent observation is that all measures show meaningful positive correlations. This outcome is known as the positive manifold, and it is commonly admitted as consistent evidence of an underlying general factor of intelligence. The positive manifold dates back to the earliest work of human intelligence with the factor analysis technique (Spearman, 1904; van der Maas et al., 2006). Some psychometric models represent a hierarchy with the general factor of intelligence (g) at the highest level, broad cognitive abilities underneath g, and narrower abilities at the next level, such as John Carroll’s three-stratum (Carroll, 1993). Other psychometric models suggest that human intelligence is non-hierarchical, with several cognitive abilities placed at the same explanatory level, such as Louis Thurstone’s primary mental abilities model (Thurstone, 1938). Figure 6.2 compares the factor structures of both models. The fluid and crystallized intelligence model (Gf ~ Gc) is another influential psychometric theory of human intelligence (Cattell, 1963, 1987). Fluid intelligence is tapped by inductive, deductive, and quantitative reasoning, representing the ability to tackle novel problems quickly and efficiently, and is thought to underlie the biological basis of human intelligence. Crystallized intelligence is tapped by tests dealing with general knowledge, the use of language, and a variety of learned skills, and is thought to underlie the environmental basis of human intelligence. Extensions of psychometric models respond to some sort of disappointment with cognitive abilities tests (Hunt, 2011). These extensions attempt to conceptualize intelligence as related to central realms of human activity, such as mental health and functioning (Das, 1999), education (Gardner, 1993), or overall success in life (Sternberg, 1999). A remarkable approach is that offered by the intelligence as process, personality, interests, and intelligence as knowledge theory (PPIK: see Figure 4.5). This theory is noteworthy because it is a comprehensive, integrative account for explaining intellectual development into maturity by outlining the interplay of other individual traits, such as personality, interests, and domain knowledge (Ackerman, 1996; Ackerman & Heggestad, 1997). The scientific study of intelligence at the information-processing level aims to examine the basic processes of intelligence that underlie individual differences in the central nervous system that are influential on the speediness in decision-making (Nettelbeck, 2011). Several elementary cognitive tasks

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intelligence Carroll’s three-stratum model

g

Gf

Gc

Gq

Gv

Glr

Gsm

Gs

g = general intelligence; Gf = fluid intelligence; Gc = crystallized intelligence; Gq = quantitative ability; Gv = visual-spatial ability; Glr = long-term storage and retrieval in memory; Gsm = short-term memory; Gs = cognitive speediness

Thurstone’s primary mental abilities model

V

W

N

S

M

P

R

V = verbal comprehension; W = verbal fluency; N = numerical ability; S = spatial ability; M = memory; P = perceptual speed; R = inductive reasoning

Figure 6.2 Hierarchical (Carroll’s model) and non-hierarchical (Thurstone’s model) psychometric models of human intelligence; the squares in both models represent the specific tests used to measure each broad factor

(ECTs) are designed to tap mental processing speed in accordance with distinct paradigms, such as reaction time (RT) and inspection time (IT), working memory, verbal comprehension, and visual-spatial reasoning processes. The performance in an ECT under one or more of these paradigms correlates with cognitive abilities calibrated with psychometric tests. A consistent body of evidence points to a significant negative correlation between speed of mental processing (i.e., RT, IT) with psychometric measures of cognitive abilities. People with higher scores in psychometric tests tend to be faster at information processing (Deary & Stough, 1996; Grudnik & Kranzler, 2001; Jensen & Munro, 1979; Johnson & Deary, 2011; Nettelbeck & Lally, 1976). Because ECTs appear to underpin individual differences in the central nervous system, information-processing theories of intelligence have been combined with psychometric and psychophysical approaches, bridging psychometric and biological theories of intelligence (Deary, 2001; Hunt, 2011). For example, the aforementioned neural efficiency hypothesis of intelligence maintains that people with higher scores in psychometric measures of

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cognitive abilities tend to show lower brain activation when performing a cognitive task than people with lower scores, who tend to show higher brain activation (Neubauer & Fink, 2009a). On the other hand, the parietofrontal integration theory of intelligence accounts for the association between individual differences in psychometric cognitive abilities with variations in brain structure and functioning (Jung & Haier, 2007). The P-FIT contends that an integrated brain network comprising predominantly areas in the parietal and frontal lobes, but also the anterior cingulate gyrus and regions in the temporal and occipital lobes, organizes the brain foundation of human intelligence. Intelligence is the psychological attribute with the greatest influence on central realms of human activity, such as work, health, and education, and also for everyday functioning in a variety of domains (Gottfredson, 1997a, 2004), but how about chess? Is a high level of intelligence a necessary requirement to perform well in the ultimate intellectual game? Are chess players more intelligent than the average population? Are stronger/expert players more intelligent than weaker/novice players are?

6.2 Individual Differences in Intelligence and Chess Chess is the prototypical intellectual game, frequently associated with intelligence in the media and society. Undoubtedly, playing chess is a demanding intellectual activity. As in other fields involving the management of complex information and abstract relationships, chess imposes an intensive use of several cognitive abilities. Earlier studies about the psychology of chess concurred reasonably well about the essential mental qualities of chess master players. Apart from youth and physical robustness, the seminal work by Binet in the late nineteenth century highlighted the importance of memory or mental calculation (Binet, 1894). Alfred Cleveland also claimed that a persistent chess memory, quickness of perception, constructive imagination, accurate and deep analysis skills, and a general mental ability were all desirable attributes for performing well in chess, while highlighting a high level of chess performance as being compatible with success in other intellectual areas (Cleveland, 1907). Cleveland also acknowledged, however, that the aforementioned abilities were rather constrained to the chess domain, and that chess skill should not be taken as a valid indicator of mental endowment (305). Besides, logical thinking, calculation speed, and imagination and will were deemed to be crucial preconditions for reaching a high level of chess performance (Djakow et al., 1927). On the other hand, de Groot highlighted that chess skill is largely determined by spatial, verbal, and learning abilities, and by an extensive knowledge base acquired from individual experience (de Groot, 1965). In addition, de Groot delved into the relationship between chess talent

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and mathematical talent, and the personality types among chess masters, by emphasizing the ‘extracurricular achievements of chess masters’. In Table 15 of his work (362–364), de Groot summarizes the chess status, training, and profession of 55 renowned grandmasters at that time. Some 24% of the players were involved in training and professions related to mathematics or hard science fields. This finding was justified because of the parallels between mathematical and chess thinking, such as spatial reasoning and mental flexibility. In contrast, however, it was also argued that, unlike mathematical thinking, chess thinking also requires permanent mental productivity, together with intuitive judgements, and decision-making under circumstances with incomplete information. Increasingly young players have dominated the world of top-level chess since the early 1970s by outperforming older players. This fact has been taken as real-world evidence for the growth in intelligence, put forward as the Flynn effect (Flynn, 1984, 1987; Howard, 1999). There are alternative explanations for the growing dominance of younger players in elite chess, however (Gobet, Campitelli, & Waters, 2002). Younger players would outperform older players not through being more intelligent but because of having more available chess information and new coaching methods, playing more frequently, starting to play earlier, and the introduction of new chess regulations concerning thinking time and tournament schemes. Further analyses with a wealth of chess data have argued that, since 1970, chess players really have achieved higher chess performance levels at progressively younger ages, however (Howard, 2005b). This age effect, observed in this latter study, was more robust within top players, which might suggest natural talent as a source of strength in accounting for individual differences in chess skill over the aforementioned changes in the chess environment. Table 6.3 summarizes similar biographical information to that provided by de Groot and Howard for unofficial and official world chess champions. It covers a span of 258 years, from François-André Danican Philidor in 1755 to Magnus Carlsen in 2013 (de Groot, 1965; Howard, 1999). This list includes leading players who were considered at the time the best chess players in the world, though the first undisputed world chess champion was Wilhelm Steinitz in 1886. For each of these twenty-six individuals, Table 6.3 displays the country of origin, the year of birth (B), the year he first won a world championship (W), the age of becoming world champion (W–B), and other intellectual activities. This information has been mainly collected from previous work from de Groot and Howard and from current specialized web pages (de Groot, 1965; Howard, 1999). Even though the number of individuals is considerably lower than that reported by de Groot, these data underline two interrelated points worth mentioning. The first point is that there are fewer intellectual or professional activities other than chess in later years. There are more players with

Table 6.3 Unofficial and official world chess champions and additional intellectual activities Champion (*)

Country

Born (B)

Win (W)

Δ(W–B)

Intellectual activities

François-André Danican Philidor Alexander Deschapelles Louis de La Bourdonnais Howard Staunton (2) Adolf Andersen (2) Paul Morphy Wilhelm Steinitz (5) Emmanuel Lasker (6) José Raúl Capablanca Alexander Alekhine (4) Machgielis Euwe Mikhail Botvinnik (5) Vasily Smyslov Mikhail Tal Tigran Petrosian (2) Boris Spassky Robert Fischer

France

1726

1755

29

Music composer

France France UK Prussia US Austria Prussia Cuba Russia Netherlands Russia Russia Latvia Georgia Russia US

1780 1795 1810 1818 1837 1836 1868 1888 1892 1901 1911 1921 1936 1929 1937 1943

1815 1834 1843 1851 1858 1866 1894 1921 1927 1935 1948 1957 1960 1963 1969 1972

35 39 33 33 21 30 26 33 35 34 37 36 24 34 32 29

Military career Chess writer Chess journalist Mathematician, high school teacher Degree in law Chess journalist Doctorate in mathematics Chemical engineering student Degree in law, chess writer Doctorate in mathematics Doctorate in electrical engineering Opera singer, chess writer Literature degree, chess writer Chess journalist Journalism degree Patent author

Table 6.3 Cont. Champion (*)

Country

Born (B)

Win (W)

Δ(W–B)

Intellectual activities

Anatoly Karpov (7) Garry Kasparov (6) Alexander Khalifman Vladimir Kramnik (3) Viswanathan Anand (5) Ruslan Ponomariov Rustam Kasimdzhanov Veselin Topalov Magnus Carlsen (4)

Russia Azerbaijan Russia Russia India Ukraine Uzbekistan Bulgaria Norway

1951 1963 1966 1975 1969 1983 1979 1975 1990

1975 1985 1999 2000 2000 2002 2004 2005 2013

24 22 33 25 31 19 25 30 23

Stamp collector, humanitarian activist Political activist, writer Chess coach Foreign languages student Bachelor of commerce Degree in law Chess coach Chess writer Entrepreneur

Note: Number in brackets indicates number of times winning the world championship.

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professional degrees between 1755 and 1960 (eight players: 31%) than between 1963 and 2013 (two players: 8%). The second point is a significant negative correlation between the individual’s birthdate and the player’s age when achieving the championship (r = –0.40, p < 0.05), indicating that the World Chess Championship has been won by increasingly younger individuals. The oldest individual included in Table 6.3 is Louis de La Bourdannais in 1834, at thirty-nine years of age, whereas the youngest world champion was Ruslan Ponomariov in 2002, when he was only nineteen years old. This is a difference in age of twenty years across two centuries. These two facts highlight that toplevel chess has become more professionalized and competitive over the years. Elite world chess has become more demanding while requiring full-time involvement in the domain. For example, the stringent conditions at toplevel competitive chess might hamper the investment of additional time and effort in ‘extra-curricular’ activities outside the chess domain. This has been conjectured in fact as a sign of lower intelligence on the part of modern chess masters, in contrast to their earlier counterparts, who had other complex interests and occupations apart from chess (Gobet et al., 2002). Besides, younger top-level chess players have been increasingly well prepared to confront and succeed against more experienced older players, though it is unlikely that this phenomenon is attributable to a generalized rise in overall intelligence, as suggested by the Flynn effect (Howard, 1999). Appendix 3 shows the studies relating a psychometric measure of human intelligence with chess skill (n = 30). The links between intelligence and chess performance evolve throughout time and are typically characterized by individual differences in both child and adult populations. This body of knowledge is summarized for the seventeen studies carried out with children, and for the ten studies carried out with adults. There were two additional studies, using the same extensive sample from the Amsterdam Chess Test that comprised both children and adults (Blanch, García, Llaveria, et al., 2017; van der Maas & Wagenmakers, 2005), and one study that compared children and adults (Schneider et al., 1993). The recorded variables for each study were the sample size, the age range, the cognitive ability, the criteria used to estimate chess skill, the study design (experimental, correlational), the male to female ratio (M:F), and the country where the study took place. The measures of cognitive abilities were derived from psychometric tests such as the WISC III, Raven’s Progressive Matrices, or the Intelligenz-Struktur-Test, or from other cognitive abilities such as processing speed, metacognitive abilities, language productivity, visual memory, abstract reasoning, and memory span. For the chess skill measure, most of the studies considered the Elo rating as the measure of chess expertise. Other measures of chess skill were derived from specific chess tests.

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6.3 Intelligence and Chess in Children There were seventeen studies with children (57%) with an age range from six to sixteen years. Six studies did not report the age range of the participants. The sample sizes ranged from twenty-four to 508, with a mean sample size of eighty-nine subjects (sd = 79). Five studies used the WISC, with three studies employing different subscales of this test, and two studies employing a general IQ test. Four studies used Raven’s Progressive Matrices (RPM). Other studies used the Primary Mental Abilities and Differential Aptitude tests (PMA, DAT), non-verbal intelligence tests (Dearborn test, TONI-3), measures of metacognitive abilities, language productivity, abstract reasoning, calculation, and an unidentified IQ measure. Seven studies used the Elo rating to gauge chess skill, whereas five studies used some sort of independent test. This makes sense, because some children in their initial chess careers might lack a reliable Elo rating. Fourteen out of the seventeen studies adopted an experimental research design (82%), whereby some sort of comparison was undertaken between chess players versus non-chess players. In contrast, only three studies adopted a correlational research design (18%). All the studies reported a remarkable predominance of boys over girls. Male to female ratios ranged from 2:1 to 10:1, whereas three studies included only boys, with 180, forty-four, and 508 participants, respectively. Regarding the geographical area, there were three studies from Spain, two studies from the United States, and one study each from the United Kingdom, the Netherlands, Belgium, Romania, Uruguay, South Korea, Iran, Argentina, Cuba, Germany, Australia, and Zaire. In the light of all the findings reported by these studies, it can be conceived that intelligence helps children to succeed in chess. More specifically, both general and visuospatial cognitive abilities are deemed to be necessary for obtaining a high level of chess skill in the group of Belgian chess players (Frydman & Lynn, 1992). In addition, the importance of visuospatial abilities in chess is also argued to be a key factor, with regard to the remarkable discrepancy in the presence of women compared to men, because women tend to score about one standard deviation below men in visuospatial abilities. Spatial and logical abilities are also considered useful for identifying chess talent in an independent study from the United States (Horgan & Morgan, 1990), with data from twenty relatively experienced chess players. This group scored significantly higher than average on the Raven’s Progressive Matrices. Besides, when comparing twenty-two chess players from Cuba with twenty-two children uninvolved in chess, it was found that the chess players scored meaningfully higher in the Wisconsin Card Sorting Test (WCST), a measure of abstract thinking (Rojas Vidaurreta, 2011). On the other hand, there is also evidence of non-significant differences in the Raven’s Progressive Matrices test when comparing two groups of chess

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players at different levels of success in competitive chess (Hernández & Rodríguez, 2006). Moreover, in the study on the recognition of chess positions with children and adults, there were no differences in the digit span memory test when comparing expert and novice chess players (Schneider et al., 1993). This sort of null effect in comparing chess experts with chess novices was also observed in an interesting study with US chess players that addressed the language productivity derived from an interview comprising three main tasks: general conversation, chess conversation, and chess explanation (Nippold, 2009). The participating children in this study were classified into eighteen novices and fourteen experts by a fifty-year-old male US Chess Federation chess master. Both groups of players produced similar amounts of language and spoke with higher levels of syntactic complexity during the chess explanation task, according to several measures of language productivity: T-units, mazes, mean length of T-units, clausal density, nominal clause use, relative clause use, and adverbial clause use. This finding somewhat contradicted the expectation of experts outperforming novices because of their greater chess knowledge and experience. Two correlational studies contrasted the joint influence of age, gender, chess experience, practice, motivation, chess enjoyment, and measures of IQ regarding their influence on chess skill. The first study (Bilalić, McLeod, & Gobet, 2007a) used an IQ measure derived from four subscales of the WISC III (vocabulary, block design, symbol search, and digit span). This measure was positively albeit moderately related to chess skill. An elite chess subsample (n = 23) scored meaningfully higher than the rest of the group in the IQ measures, however. In addition, it turned out that the IQ measure related negatively to chess skill, suggesting that children scoring higher in the IQ measure had a lower level of chess skill, and highlighting the lack of a clear influence of cognitive ability on chess skill. Another remarkable finding was that, within this elite subsample, children with higher IQ scores practised chess to a lesser extent than children with lower IQ scores, rendering practice the strongest predictor of chess skill. The overall findings of the study conclude that a combination of factors such as practice, experience, age, and gender were the most likely to impinge on chess skill. The second study, with twenty-two children who were newcomers to the field of chess, used the same WISC III vocabulary, block design, symbol search, and digit span subscales as in the study by Merim Bilalić et al., together with an overall IQ measure (de Bruin et al., 2014). The main findings in this latter study indicated a strong influence by the IQ measure on chess skill, whereas practice had a somewhat lower, albeit meaningful, effect on chess skill. Moreover, motivation had a notable indirect effect on chess skill, through practice. Children who reported higher motivational levels were those reporting higher dedication to playing chess while being more involved in practice activities. The findings from these two latter studies support two main conclusions. First, cognitive ability is particularly

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influential for chess performance at the earlier stages of chess learning. In contrast, practice is likely to be particularly influential at progressively later stages of chess learning. Second, apart from cognitive ability, practice, age, gender, and motivation are plausible determinants of individual differences in chess skill. The impression that chess bears several desirable properties thought to stimulate children’s cognitive development is quite popular and prevalent worldwide. There is a field of research that has addressed this topic with enthusiasm. For example, when comparing school-age children who played chess with school-age children who did not play chess, studies from Uruguay (Grau-Pérez & Moreira, 2017), Argentina (Ramos, Arán, & Krumm, 2018), and Cuba (Rojas Vidaurreta, 2011) employed similar measures of executive functions, such as the WCST or the Stroop test. These three studies converge in arguing that chess might have a meaningful impact on the development of cognitive functioning at early ages. The implicit underlying idea within this contention is that practising chess at early life stages may be stimulative of a number of complex problem-solving abilities amenable to generalize and transfer to other circumstances. Analogous findings have been reported in two studies with an extensive sample of Spanish chess players (Aciego, García, & Betancort, 2012, 2016). These studies compared 170 children involved in chess with sixty children involved in soccer or basketball as extra-curricular activities. Children were evaluated twice with the WISC-R, and with the Multifactor Self-Assessment Test of Child Adjustment (TAMAI), which taps personal, social, family, and school adjustment. The first assessment (pre-test) took place towards the beginning of the school year, and the second assessment (post-test) at the end of the school year, approximately nine months later. In the first study (Aciego et al., 2012), greater improvements in the chess group between both assessments were reported in several of the studied areas. Children in the chess group obtained significantly higher scores in the similarities, digits, block design, object assembly, and maze subtests of the WISC-R, and also in the personal and school adjustment TAMAI subtests. A similar group comparison design was undertaken in the second study, though the chess group was additionally split into a group focused on chess to spur mental skills and social values, and another group focused on the sporting side of chess (Aciego et al., 2016). Again, meaningful improvements were higher in the chess groups compared with the soccer or basketball group. Furthermore, for the chess group with an instructional method addressing mental skills and social values, the improvements were found in both cognitive and adjustment variables. For the chess group emphasizing the teaching of chess on the sporting side, the improvements were limited to the cognitive variables. Further similar studies have yielded debatable results. A research design with twenty Romanian chess players compared with a control group of

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eighteen students, for example, reports that there were no differences between both groups in an IQ test, in an auditory word memory test, and in digit memory tests (Gliga & Flesner, 2014). In contrast, the chess group had a greater improvement than the control group in academic achievement in mathematics and language. Another study, with a more extensive sample size of 180 male students from Iran, allocated at random eighty-six students to a six-month chess course and another group of ninety-four students to a control group (Kazemi, Yektayar, & Abad, 2012). Both groups were evaluated in metacognitive abilities and mathematical problem solving. Higher meaningful improvements are reported for the group taking the chess course than for the control group, in both metacognitive abilities and mathematical problem solving, suggesting the usefulness of chess in promoting higher-order thinking skills. Controversial findings have also been reported by studies describing chess instructional interventions aimed at improving the cognitive abilities of children with special needs. A study in South Korea investigated whether chess had beneficial effects in students at risk of academic failure. A ninety-minute chess programme was delivered once a week over three months to a randomly selected group of eighteen students and a control group following regular teaching activities (Hong & Bart, 2007). No cognitive effects measured by the Raven’s Progressive Matrices test and a test of non-verbal intelligence were detected as a consequence of the chess instructional programme. The observed changes in the experimental group were very similar to those observed in the control group. These outcomes were partly attributed to the limited time devoted to the chess intervention, however, and to the failure of the participants to reach a minimum level of chess skill. In contrast, another study from Germany analysed whether a chess instruction intervention extending throughout a whole academic year might improve the calculation and concentration abilities of students in the low range (70 to 85) of IQ scores (Scholz et al., 2008). This study assigned a random class of thirty-one students to the chess instruction, consisting of one weekly hour of chess lessons (experimental group), while twenty-two students followed their regular classes. There was a meaningful improvement in simple addition, counting, and calculation abilities, but not in concentration abilities. The study emphasized the learning value of chess for children with learning disabilities, and that skills derived from chess lessons were somehow transferred to improving basic mathematical skills. The conclusions from the studies arguing for meaningful improvements in cognitive abilities through chess training appear extremely positive in terms of underlining the potential benefits of chess. The findings should be taken with a substantial amount of caution, however. Several issues have been raised that suggest the need for considerable scepticism with regard to most findings from this field of research (Bart, 2014; Gobet & Campitelli, 2006; Sala, Foley, &

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Gobet, 2017; Sala & Gobet, 2016). For example, a meta-analysis with twentyfour studies addresses whether there were transfer effects from chess instruction to academic and cognitive skills. None of the examined studies used a research design covering a combination of critical aspects such as the inclusion of pre-test and a post-test analysis, the random allotment of participants to different experimental conditions, or the inclusion of placebo and active-control groups (Sala & Gobet, 2016). An additional problem with studies reporting significant improvements in cognitive abilities when comparing chess players with other groups of students is that concerning the issue of statistical power. Most of these studies adopting a comparative approach base their conclusions on findings from tests contrasting binary hypotheses: a null hypothesis stating no differences between groups against an alternative hypothesis stating differences between groups. The power of such statistical contrasts is the probability of rejecting the null hypothesis when the alternative hypothesis is true. Thus, high levels of power are desirable in a typical t-test that compares whether one group of chess players improves in cognitive abilities from a pre-test to a post-test, or whether a group of chess players improves in cognitive abilities compared with a group of students unacquainted with chess. Unfortunately, these kinds of statistical contrasts might be very underpowered, particularly when relying on small sample sizes, which were the most commonly used in these designs, or when the studied groups have very different sample sizes (Cohen, 1988). Ideally, these kinds of comparative designs ought to render a power analysis prior to the actual data collection. A study applying data analyses techniques that were more sophisticated while incorporating a larger sample size yields contradictory findings to those highlighting the benefits of chess for the cognitive and academic development of schoolchildren. This study was undertaken with over 500 Australian students from grades 6 to 12, including sixty-four regular chess players. The study was not limited to a t-test comparison. More specifically, it used item response theory and hierarchical linear modelling to evaluate the effect of playing chess on individual differences in scientific thinking in the framework of the Australian Schools Science Competition (Thompson, 2003). This study found no evidence for the hypothesis that playing chess leads to improved scientific thinking. Instead, these findings from Australia indicate that grade level and IQ are far stronger predictors of scientific thinking than playing chess, explaining over 50% of the variability in science scholastic performance. The problem of whether chess has benefits for educational attainment and cognitive development is further explored in Chapter 10, which summarizes the application of several chess instructional interventions aimed at improving academic achievement and other desirable attributes for children.

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6.4 Intelligence and Chess in Adults There have been ten studies with adults (33%) with an age range from fifteen to eighty-one years. Three studies did not report the age range of the participants. The sample sizes used in the studies with adults ranged from twenty-nine to ninety, with a mean of forty-four subjects (sd = 19). Four studies used the Raven’s Progressive Matrices (RPMs), two studies used the IntelligenzStruktur-Test, two studies used measures of visual memory, and one study used the Berlin Structural Model of Intelligence, the WAIS, and a measure of processing speed. Unlike the research works with children, all studies with adults measured chess skill with the Elo rating. Like the studies with children, however, most studies with adults employed an experimental research design (eight: 80%), while only two studies adopted a correlational research design (20%). Similarly, the same predominance of males was also observed here, with male to female ratios ranging from 2:1 to 33:1, and with two studies including only male participants. Concerning the geographical area, there were three studies from Germany, two studies from Austria and China, and one study each from Switzerland, the United States, and the United Kingdom. Two brain-imaging studies used the RPMs and a measures of visuospatial abilities as a control variable (Duan et al., 2012; Hanggi et al., 2014). The study by Duan and collaborators compared fifteen master-level chess players with fifteen novice-level chess players (n = 15). Similarly, the study by Hanggi and collaborators compared a group of twenty expert players with a group of twenty men unfamiliar with chess. Both studies report that the two groups under scrutiny scored very similarly in the psychometric measures of cognitive ability, without bearing statistically significant differences. Both studies also report remarkable brain anatomical differences, however. Expert players compared with novice players had smaller caudate nuclei, and a more extensive default brain network (Duan et al., 2012). In addition, chess players compared with controls had lower grey matter volume in the occipito-parietal junction, but very similar volumes in the caudate nucleus (Hanggi et al., 2014). These two studies attempt to explain these findings in terms of a synaptic pruning mechanism thought to elicit a more efficient integration of brain functioning (see Chapter 5). Very similar findings regarding intelligence measures have also been reported when comparing a group of twenty-five German chess players with a control group of twenty-five non-chess players (n = 25) matched on age and educational level (Unterrainer et al., 2006, 2011). Both groups scored similarly in fluid abilities, or in verbal and visuospatial working memory. An additional evaluation of planning abilities was conducted with the Tower of London test, a neuropsychological test gauging planning abilities, in which chess players outperformed non-chess players. This outcome was particularly manifest for more difficult problems, whereby chess players also showed longer planning

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and movement execution times. One important consideration derived from this work was whether motivational or strategic differences might partially explain these findings, a topic addressed in a subsequent study from the same research group with a similar paradigm (Unterrainer et al., 2011). Another group of thirty experienced chess players were compared with a control group of thirty people in Experiment 1. Eighteen months later, in Experiment 2, twenty-two of the same chess players as those participating in Experiment 1 were compared again, with nineteen controls. The Tower of London test was applied with time restrictions in Experiment 1, and without time restrictions in Experiment 2. This study yielded no significant differences between chess players and non-players, irrespective of the time constraints imposed in each of the two experiments. Chess players reported a higher level of trait and state motivation across both experiments, however. On the other hand, the overall outcomes suggested that planning performance is equivalent in chess players and controls, running counter to the idea of transfer of chess planning to a different cognitive domain. Visuospatial abilities have been routinely thought to be very relevant for chess playing, according to studies about mental imagery in blindfold chess (Saariluoma & Kalakoski, 1997; Saariluoma et al., 2004) and studies about intelligence and chess playing in children (Frydman & Lynn, 1992; Horgan & Morgan, 1990). Whether visuospatial abilities relate explicitly to chess skill in adults was studied by evaluating a group of thirty-six British chess players on a visual memory test (Waters, Gobet, & Leyden, 2002). Master-level players performed the same as non-master-level players, however, and the same as a broad normative sample of 550 US Navy recruits in this test. The performance in the visual memory test was in addition uncorrelated with chess skill as measured by the British Chess Federation rating. The possibility that the lack of correlation between the visual memory test and chess skill could be due to a restriction of range in the chess skill measure was disregarded because of the relatively wide range in these data. Alternatively, it was argued that this discrepancy with previous findings could depend on the narrower nature of the cognitive ability used (i.e., visual memory test versus WISC subscale), and on the sample background (i.e., adults versus children). Although these findings indicate that visuospatial abilities might be relatively unimportant for the acquisition of chess skill and expertise in the long term, further evidence supports the view that there are meaningful individual differences regarding the association of other cognitive abilities with chess skill. For example, one of the very first psychometric studies about the intelligence of chess players (Doll & Mayr, 1987) reports significant differences in measures of cognitive abilities between a group of twenty-seven expert chess players, with Elo ratings between 2220 and 2425, and a normative sample (n = 204). Chess players scored significantly higher than the normative sample in processing speed, information processing, and numerical abilities, but also in general intelligence

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as measured by the Berlin Structural Model of Intelligence (BIS) and the Culture Fair Intelligence (CFT-3) tests. The BIS comprises three main broad factors (verbal, figural, and numerical), obtained through many different tasks, and a general measure of intelligence. The CFT-3 is a measure of fluid intelligence, comprising inductive reasoning tasks based on geometric figures. On the other hand, the intelligence test scores were uncorrelated with the Elo ratings, probably because of the restriction of range in the observed measures of chess skill. Moreover, there are remarkable individual differences in the perceptual processing ability of chess positions. The advantage of experts over novices has been attributed to higher levels of chess experience and knowledge (Kiesel et al., 2009; Reingold et al., 2001), and to the greater familiarity of experts regarding specific meaningful arrangements of chess positions (Bilalić, McLeod et al., 2009; Schneider et al., 1993). The recognition of check and threat events in several chess positions was addressed by evaluating age effects and information-processing speed with the Digit Symbol Substitution Test from the WAIS (Jastrzembski, Charness, & Vasyukova, 2006). A group of twenty-nine young chess players between seventeen and forty-four years of age was compared with a group of thirty older chess players between forty-five and eighty-one. Slower responses from older players were expected because of decrements in information-processing abilities with ageing, although a weaker effect at higher levels of expertise was hypothesized. Nevertheless, the chess skill level did not ameliorate age-related effects on the speed of detection of checks and threats, suggesting that knowledge activation processes tend to become slower with age even for expert players. The most comprehensive studies of intelligence and chess playing, however, were probably those performed with Austrian chess players (Grabner et al., 2006, 2007). These works are noteworthy because they comprise elements from the three levels of analysis and measurement in differential psychology, including a psychometric testing of traits, experimentation about cognitive processes, and psychophysiological recordings of the biological organism (see Figure 4.3). In the first study (Grabner et al., 2006), the EEG alpha-band eventrelated desynchronization method characterized the degree and topographical distribution of cortical activation of a substantial sample with forty-seven chess players. The study tested the neural efficiency hypothesis, which predicts that more intelligent people tend to display lower brain activation than less intelligent people when challenged with a cognitively demanding task (Neubauer & Fink, 2009a). The psychometric measures of intelligence were derived from the Intelligenz-Struktur-Test 2000 R, comprising measures of verbal, numerical, figural, and general cognitive abilities. There were three experimental chessrelated tasks. First, the speed task consisted of determining the presence of certain chess pieces on the chessboard in a fast and accurate way. Second, the memory task stipulated the memorization of chess positions presented briefly for ten seconds. Third, the reasoning task involved solving a checkmate or

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chess-planning problem. The study applied an extended expert–novice paradigm, splitting the sample into four groups: (1) a lower-IQ group (n = 23; M = 106 [Sd = 9]); (2) a higher-IQ group (n = 24; M = 129 [Sd = 6]); (3) a lower-Elo-rating group (n = 24; M = 1717 [Sd = 164]); and (4) a higher-Elo-rating group (n = 23; M = 2076 [Sd = 105]). The findings in the study are aligned with the NEH. Chess players with higher scores in cognitive abilities displayed more efficient brain functioning than their colleagues with lower scores in cognitive abilities did. These individual differences were particularly evident concerning the prefrontal cortex. In addition, players with a higher level of skill in the memory and reasoning tasks also had lower activation of the frontal cortices, even with higher activation of the parietal cortices. Hence, the view is that, rather than depending on domainspecific competences and knowledge, chess performance depends largely on the general efficiency of the information-processing system. In the second study (Grabner et al., 2007), a large sample of ninety tournament players with a mean Elo rating of 1869 (Sd = 247) completed several psychometric measures in intelligence, personality, motivation, and emotional competences. Moreover, the study evaluated individual differences in chess attitudes and chess practice activities. When submitting all these factors to a predictive analysis, several variables contributed to the observed individual differences in chess skill. Numerical cognitive abilities, age at entering the domain, age, number of tournament games played between 2002 and 2005, control over the expression of emotions, and motivation explained a substantial 55% of the variability in the Elo chess rating. Further additional analyses of these data addressed the association of fluid and crystallized abilities (Cattell, 1963, 1987) and their relationship to the Elo rating (Grabner, 2014a). Fluid intelligence includes subscales about sentence completion, analogies, finding similarities, arithmetic problems, number series, arithmetic operators, figure selection, cube task, and matrices. Crystallized intelligence included knowledge subscales in the general domain, and in verbal, numerical, and figural domains. Several of these subscales correlated meaningfully with the Elo rating, ranging from 0.28 to 0.44 for fluid abilities, and from 0.24 to 0.45 for crystallized abilities, and with higher correlations for number series (0.44) and numerical knowledge (0.45). Overall, these findings definitely support the view that the level of chess skill depends not only on cognitive abilities but also on individual differences in other variables.

6.5 Summarizing Findings about Intelligence in Chess An in-depth review comprising the extant body of research into intelligence and chess highlights two important themes. First, expert chess players have only a modestly higher level of intelligence than control groups. Second, a chess player’s strength, usually measured with the Elo chess rating, relates

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moderately to the level of intelligence (Grabner, 2014a). This overall review encompasses a few additional points to bear in mind. 1. Intelligence is far from being the best predictor of chess performance. An important proportion of individual differences in chess performance can be accounted for by practice within the domain. 2. Intelligence can influence the development of chess expertise in two ways. First, a minimum level of intelligence is needed to accomplish a high level of chess performance. Beyond that point, individual differences in nonability factors (i.e., personality, motivation, and concentration) determine peak performance. Second, intelligence is particularly important in the earlier stages of chess expertise development, and its influence decreases in the later stages. 3. Individual differences in visuospatial abilities relate more strongly to chess skill and chess training performance in children than in adults. 4. There are several methodological limitations in this body of research, namely a lack of larger representative samples, a range restriction in the measures of cognitive abilities, the need for a more comprehensive measurement of cognitive abilities, and the ignoring of individual differences in practice, experience, age, gender, and personality. Much of this body of research into intelligence and chess has been meta-analytically reviewed in a more recent study focusing on the relationship between cognitive ability and chess skill (Burgoyne et al., 2016). This meta-analysis involved three main questions: (1) whether more skilled players scored higher in cognitive abilities tests than less skilled players; (2) whether this relationship varied with age; and (3) whether this relationship varied with the content of the cognitive ability measure (i.e., visuospatial, numerical, or verbal). Cognitive ability was conceptualized here in accordance with the Cattell–Horn–Carroll (CHC) psychometric model (McGrew, 2009), contemplating a general factor (g), and four broad factors: fluid reasoning (Gf), comprehension-knowledge (Gc), shortterm memory (Gsm), and processing speed (Gs). The main findings with regard to the association of cognitive abilities with chess skill are as follows. 1. A rather moderate association, which is somewhat similar regarding the four broad factors of cognitive ability (Gf, Gc, Gsm, and Gs), though very low for the general intelligence or g factor. 2. The association of cognitive abilities with chess skill is stronger for unskilled or unranked samples than for samples formed by more skilled or ranked players. 3. The association of cognitive abilities with chess skill is stronger for child and youth samples than for adult samples.

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4. The association of cognitive abilities with chess skill is stronger for numerical ability content, intermediate for verbal ability content, and weak for visuospatial ability content. Altogether, the findings from this meta-analysis are rather inconclusive about the association of chess skill with cognitive ability. Despite the fact that chess skill correlates positively with the cognitive abilities of choice, a considerable amount of the variability in chess skill (mostly over 90%) goes unaccounted for by cognitive abilities. The limited amount of studies involved could be a noteworthy drawback, however, in terms of impairing the stability of the meta-analytic results (Rosenthal, 1995). For example, the rather low number of studies (n = 19) stands in sharp contrast to other meta-analyses of topics involving cognitive abilities, such as those for the Flynn effect, with n = 285 studies (Trahan et al., 2014), or gender differences in mathematical performance, with n = 242 studies (Lindberg et al., 2010). This limitation concerning the amount of studies included in a meta-analysis has also been highlighted in another meta-analytic review with only n = 7 studies comparing chess players with non-chess players (Sala, Burgoyne, et al., 2017). This study evaluates the academic selection hypothesis, postulating that the differences in cognitive abilities between experts and non-experts are due to the training opportunities involved in access to formal academic training. Because chess lacks such an effect, unlike the admission tests to several education programmes, meaningful differences in cognitive abilities between chess players and non-chess players should record the true impact of cognitive abilities in expertise. The main findings of this meta-analysis in fact suggests an advantage in the cognitive abilities of chess players over non-chess players, implying that cognitive ability is an important explanatory factor in the development of chess skill. Hence, and taken together, the findings from this body of knowledge suggest that the evidence attempting to link cognitive abilities to chess expertise is inconclusive and, at times, contradictory. One possible reason for this outcome stems from the idea that chess performance may largely depend on the combination and synergies of individual differences in several traits or broad clusters of traits, as suggested by the PPIK theory (Figure 4.5) (Ackerman, 1996; Ackerman & Heggestad, 1997). Individual differences in ability, but also in non-ability factors such as personality and interests, may play a role in determining individual differences in chess performance. In the next section, this question is examined with part of the data from the sample used in the development of the Amsterdam Chess Test.

6.6 Chess Skill versus Chess Motivation in Predicting Chess Performance Individual differences in cognitive abilities are, obviously, important for chess performance. The seminal work by de Groot puts forward some of the main

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areas whereby individual differences should emerge in the elicitation of chess talent (de Groot, 1965), which include but are not limited to higher scores in cognitive and learning abilities, an extensive knowledge base, and deep motivation. The PPIK provides a theoretical framework useful to address adult intellectual development (Ackerman, 1996; Ackerman & Heggestad, 1997), comprising four main clusters of traits (see Figure 4.5): intelligence as process (Gf), personality, interests, and intelligence as knowledge (Gc). On the other hand, contemporary empirical works examining the interrelationship of cognitive abilities with chess skill and chess performance, in both children and adults, find that the evidence remains elusive, resulting in calls for comprehensive studies incorporating a wider array of individual differences comprehending practice factors and non-ability traits (Bilalić, McLeod, & Gobet, 2007b; de Bruin et al., 2014; Grabner et al., 2007). For example, the findings from Austrian chess players contemplated factors belonging to domains other than intelligence, such as experience and chess practice activities, personality, emotional competences, motivation, or attitudes. These findings are in accordance with earlier approaches to explaining chess thinking, which argue for the complex interplay of emotional, motivational, and cognitive processes (Tikhomirov & Vinogradov, 1970). In this section, chess skill and chess motivation are compared with regard to their influence on performance in three main kinds of chess problems: tactical, positional, and endgames. More specifically, the analysis looks at whether chess skill or chess motivation are more predictive of chess performance when embedded together in the same predictive model. The data for this analysis were taken from the Amsterdam Chess Test (van der Maas & Wagenmakers, 2005). The chess players were those with complete data in all measures selected for the current analyses (n = 225). These players had a mean age of thirty-one years (Sd = 15), ranging between eleven and seventy-eight, and a mean Elo rating of 1870 points (Sd = 293), ranging between 1169 and 2629 points. Apart from the Elo rating, the measures were the motivation questionnaire, and the performance in the two tests from the choose-a-move subtask (see Figure 4.6). The thirty-item motivation questionnaire measures three motivation-related traits – positive fear of failure, negative fear of failure, and desire to win – even though a global motivation score was used here. Ten seconds were allotted to complete each of these items, which were answered on a five-point disagree/agree scale. The choose-a-move A and B subtasks contain forty chess problems depicted in chessboards, and including twenty tactical items, ten positional items, and ten endgame items. There was a time limit of thirty seconds to complete each item. A correct answer to an item scored one point, while wrong answers scored zero points. Higher scores in the motivation questionnaire and in the choose-a-move A and B tasks indicated higher motivational

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levels, and superior performance in the tactical, positional, and endgame chess-playing dimensions, respectively. The influence of chess skill as measured by the Elo rating and of the motivation measure on the tactical, positional, and endgame performance was evaluated with a structural equation model with latent variables – i.e., conceptual unobservable constructs that are measured with observed indicators (Bollen, 1989). This technique allows for the simultaneous specification and estimation of complex causal relationships between several variables. The specification of this model is shown at the top of Figure 6.3. There were two observed variables (chess skill and motivation), and three latent variables (tactical, positional, and endgame) measured by the two test forms of the choose-a-move subtask, A and B. Chess skill and motivation were specified as correlated, because higher Elo scores related to higher motivation scores (r = 0.21, p < .001). The model was specified and estimated with the maximumlikelihood robust method implemented with the lavaan package from the R software (R Development Core Team, 2015; Rosseel, 2012). Three different models were compared concerning the effects of chess skill and motivation on the tactical, positional, and endgame performance. Model 1 evaluated the concurrent effects of both chess skill and motivation. Model 2 evaluated the effects of chess skill only by setting the effects of motivation on tactical, positional, and endgame variables to zero. Model 3 evaluated the effects of motivation only by setting the effects of chess skill on tactical, positional, and endgame variables to zero. The effects represented with numbers are to be interpreted as regression coefficients, although, in a structural equation modelling context, are commonly referred to as beta weights (Bollen, 1989). The three models were additionally compared with a chi-square difference test (Δχ2). Assuming a correct model specification, a significant difference in comparing two models (p < 0.05) would support the most parsimonious model with the lower amount of degrees of freedom (Yuan & Bentler, 2004). The main findings are shown at the bottom of Figure 6.3. Model 1 shows that the effects of chess skill were highly significant on each kind of performance: tactical (0.79), positional (0.85), and endgame (0.89). In contrast, the effects of motivation were significant only with regard to tactical performance (0.18, p < 0.001), albeit with a much lower magnitude. The coefficients of determination (R2) indicate that the explained variability in each kind of performance was large: 71% for tactical performance, 75% for positional performance, and the largest – 81% – of the accounted variance for the endgame performance. The model fit indices were good (Hu & Bentler, 1999), suggesting that the specified model did indeed represent the observed data well (CFI = 0.991, TLI = 0.979, RMSEA = 0.061, AIC = 4,014). The Model 2 findings show that, when the effects of motivation on the tactical, positional, and endgame latent variables were set to zero, there was a meaningful worsening of model fit when compared with Model 1, with a significant chi-square difference: Δχ2[3] = 15.18, p = 0.0017. Model 2 shows

skill or motivation in predicting chess performance Tactical (T)

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A B

Chess skill Positional (P)

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Motivation Endgame (E)

χ2

Model 1

Model 2

22.02*

37.20

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Model 3 281.85***

CFI

.991

.980

.759

TLI

.979

.962

.550

RMSEA

.061

.083

.286

4,014

AIC T

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4,024 E

Chess skill .79*** .85*** .89*** Motivation .18* .05 .04 R2

.71

.75

81

T

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4,276 E

.83*** .86*** .90*** ---

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.68

.74

.81

T

P

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.34*** .23** .12

.05

E --.23** .05

Figure 6.3 Structural equation model evaluating the impact of chess skill (Elo rating) and motivation, on tactical (T), positional (P), and endgame (E) chess performance; observed variables are represented with squares, latent (unobserved) variables are represented with ellipses; one-headed arrows represent causal links, the two-headed arrow a correlation; there were twelve degrees of freedom for Model 1, and fifteen degrees of freedom for Models 2 and 3 (CFI = comparative fit index; TLI = Tucker– Lewis index; RMSEA = root mean squared error of approximation; AIC = Akaike information criterion) Notes: * p < 0.05; ** p < 0.01; *** p < 0.001.

that the fit indices were still acceptable (CFI = 0.980, TLI = 0.962, RMSEA = 0.083, AIC = 4,024), that chess skill had a meaningful impact on the tactical, positional, and endgame latent variables, and that chess skill explained a considerable amount of variance in the three latent variables. The Model 3 findings show that, when the effects of chess skill on the tactical, positional, and endgame latent variables were set to zero, there was an even stronger deterioration in model fit when compared with Model 1, with a highly significant chi-square difference: Δχ2[3] = 259.83, p